ForecasterRecursiveMultiSeries

skforecast.recursive._forecaster_recursive_multiseries.ForecasterRecursiveMultiSeries

ForecasterRecursiveMultiSeries(
    regressor,
    lags=None,
    window_features=None,
    encoding="ordinal",
    transformer_series=None,
    transformer_exog=None,
    weight_func=None,
    series_weights=None,
    differentiation=None,
    dropna_from_series=False,
    fit_kwargs=None,
    binner_kwargs=None,
    forecaster_id=None,
)

Bases: ForecasterBase

This class turns any regressor compatible with the scikit-learn API into a recursive autoregressive (multi-step) forecaster for multiple series.

Parameters:

Name	Type	Description	Default
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API.	required
lags	int, list, numpy ndarray, range	Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1. int: include lags from 1 to lags (included). list, 1d numpy ndarray or range: include only lags present in lags, all elements must be int. None: no lags are included as predictors.	None
window_features	(object, list)	Instance or list of instances used to create window features. Window features are created from the original time series and are included as predictors.	None
encoding	(str, None)	Encoding used to identify the different series. If 'ordinal', a single column is created with integer values from 0 to n_series - 1. If 'ordinal_category', a single column is created with integer values from 0 to n_series - 1 and the column is transformed into pandas.category dtype so that it can be used as a categorical variable. If 'onehot', a binary column is created for each series. If None, no column is created to identify the series. Internally, the series are identified as an integer from 0 to n_series - 1, but no column is created in the training matrices. Changed to 'ordinal' in version 0.14.0	'ordinal'
transformer_series	(transformer(preprocessor), dict)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. Transformation is applied to each series before training the forecaster. ColumnTransformers are not allowed since they do not have inverse_transform method. If single transformer: it is cloned and applied to all series. If dict of transformers: a different transformer can be used for each series.	None
transformer_exog	transformer	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API. The transformation is applied to exog before training the forecaster. inverse_transform is not available when using ColumnTransformers.	None
weight_func	(Callable, dict)	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. See Notes section for more details on the use of the weights. If single function: it is applied to all series. If dict {'series_column_name' : Callable}: a different function can be used for each series, a weight of 1 is given to all series not present in weight_func.	None
series_weights	dict	Weights associated with each series {'series_column_name' : float}. It is only applied if the regressor used accepts sample_weight in its fit method. See Notes section for more details on the use of the weights. If a dict is provided, a weight of 1 is given to all series not present in series_weights. If None, all levels have the same weight.	None
differentiation	(int, dict)	Order of differencing applied to the time series before training the forecaster. The order of differentiation is the number of times the differencing operation is applied to a time series. Differencing involves computing the differences between consecutive data points in the series. Before returning a prediction, the differencing operation is reversed. If int, the same order of differentiation is applied to all series. If dict, a different order of differentiation (including None) can be used for each series. The keys must be the names of the series used to fit the forecaster. If a series is not present in the dictionary, no differencing is applied. If None, no differencing is applied.	None
dropna_from_series	bool	Determine whether NaN detected in the training matrices will be dropped. If True, drop NaNs in X_train and same rows in y_train. If False, leave NaNs in X_train and warn the user. New in version 0.12.0	False
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.	None
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner used to discretize the residuals into k bins according to the predicted values associated with each residual. Available arguments are: n_bins, method, subsample, random_state and dtype. Argument method is passed internally to the function numpy.percentile. New in version 0.14.0	None
forecaster_id	(str, int)	Name used as an identifier of the forecaster.	None

Attributes:

Name	Type	Description
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API.
lags	numpy ndarray	Lags used as predictors.
lags_names	list	Names of the lags used as predictors.
max_lag	int	Maximum lag included in lags.
window_features	list	Class or list of classes used to create window features.
window_features_names	list	Names of the window features to be included in the X_train matrix.
window_features_class_names	list	Names of the classes used to create the window features.
max_size_window_features	int	Maximum window size required by the window features.
window_size	int	The window size needed to create the predictors. It is calculated as the maximum value between max_lag and max_size_window_features. If differentiation is used, window_size is increased by n units equal to the order of differentiation so that predictors can be generated correctly.
encoding	str	Encoding used to identify the different series. If 'ordinal', a single column is created with integer values from 0 to n_series - 1. If 'ordinal_category', a single column is created with integer values from 0 to n_series - 1 and the column is transformed into pandas.category dtype so that it can be used as a categorical variable. If 'onehot', a binary column is created for each series. If None, no column is created to identify the series. Internally, the series are identified as an integer from 0 to n_series - 1, but no column is created in the training matrices. Changed to 'ordinal' in version 0.14.0
encoder	preprocessing	Scikit-learn preprocessing encoder used to encode the series. New in version 0.12.0
encoding_mapping_	dict	Mapping of the encoding used to identify the different series.
transformer_series	(transformer(preprocessor), dict)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. Transformation is applied to each series before training the forecaster. ColumnTransformers are not allowed since they do not have inverse_transform method. If single transformer: it is cloned and applied to all series. If dict of transformers: a different transformer can be used for each series.
transformer_series_	dict	Dictionary with the transformer for each series. It is created cloning the objects in transformer_series and is used internally to avoid overwriting.
transformer_exog	transformer(preprocessor)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API. The transformation is applied to exog before training the forecaster. inverse_transform is not available when using ColumnTransformers.
weight_func	(Callable, dict)	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. See Notes section for more details on the use of the weights. If single function: it is applied to all series. If dict {'series_column_name' : Callable}: a different function can be used for each series, a weight of 1 is given to all series not present in weight_func.
weight_func_	dict	Dictionary with the weight_func for each series. It is created cloning the objects in weight_func and is used internally to avoid overwriting.
source_code_weight_func	(str, dict)	Source code of the custom function(s) used to create weights.
series_weights	dict	Weights associated with each series {'series_column_name' : float}. It is only applied if the regressor used accepts sample_weight in its fit method. See Notes section for more details on the use of the weights. If a dict is provided, a weight of 1 is given to all series not present in series_weights. If None, all levels have the same weight.
series_weights_	dict	Weights associated with each series. It is created as a clone of series_weights and is used internally to avoid overwriting.
differentiation	(int, dict)	The order of differencing applied to the time series prior to training the forecaster.
differentiation_max	int	Maximum order of differentiation.
differentiator	(TimeSeriesDifferentiator, dict)	Skforecast object (or dict of objects) used to differentiate the time series.
differentiator_	dict	Dictionary with the differentiator for each series. It is created cloning the objects in differentiator and is used internally to avoid overwriting.
dropna_from_series	bool	Determine whether NaN detected in the training matrices will be dropped.
last_window_	dict	Last window of training data for each series. It stores the values needed to predict the next step immediately after the training data. These values are stored in the original scale of the time series before undergoing any transformations or differentiation. When differentiation parameter is specified, the dimensions of the last_window_ are expanded as many values as the order of differentiation. For example, if lags = 7 and differentiation = 1, last_window_ will have 8 values.
index_type_	type	Type of index of the input used in training.
index_freq_	str	Frequency of Index of the input used in training.
training_range_	dict	First and last values of index of the data used during training for each series.
series_names_in_	list	Names of the series (levels) provided by the user during training.
exog_in_	bool	If the forecaster has been trained using exogenous variable/s.
exog_names_in_	list	Names of the exogenous variables used during training.
exog_type_in_	type	Type of exogenous data (pandas Series, DataFrame or dict) used in training.
exog_dtypes_in_	dict	Type of each exogenous variable/s used in training. If transformer_exog is used, the dtypes are calculated before the transformation.
X_train_series_names_in_	list	Names of the series (levels) included in the matrix X_train created internally for training. It can be different from series_names_in_ if some series are dropped during the training process because of NaNs or because they are not present in the training period.
X_train_window_features_names_out_	list	Names of the window features included in the matrix X_train created internally for training.
X_train_exog_names_out_	list	Names of the exogenous variables included in the matrix X_train created internally for training. It can be different from exog_names_in_ if some exogenous variables are transformed during the training process.
X_train_features_names_out_	list	Names of columns of the matrix created internally for training.
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.
in_sample_residuals_	dict	Residuals of the model when predicting training data. Only stored up to 10_000 values per series in the form {series: residuals}. If transformer_series is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
in_sample_residuals_by_bin_	dict	In sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ per series in the form {series: residuals}. If transformer_series is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation. New in version 0.15.0
out_sample_residuals_	dict	Residuals of the model when predicting non-training data. Only stored up to 10_000 values per series in the form {series: residuals}. Use set_out_sample_residuals() method to set values. If transformer_series is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
out_sample_residuals_by_bin_	dict	Out of sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ per series in the form {series: residuals}. If transformer_series is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation. New in version 0.15.0
binner	dict	Dictionary of skforecast.preprocessing.QuantileBinner used to discretize residuals of each series into k bins according to the predicted values associated with each residual. In the form {series: binner}. New in version 0.15.0
binner_intervals_	dict	Intervals used to discretize residuals into k bins according to the predicted values associated with each residual. In the form {series: binner_intervals_}. New in version 0.15.0
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner. New in version 0.15.0
creation_date	str	Date of creation.
is_fitted	bool	Tag to identify if the regressor has been fitted (trained).
fit_date	str	Date of last fit.
skforecast_version	str	Version of skforecast library used to create the forecaster.
python_version	str	Version of python used to create the forecaster.
forecaster_id	(str, int)	Name used as an identifier of the forecaster.
_probabilistic_mode	(str, bool)	Private attribute used to indicate whether the forecaster should perform some calculations during backtesting.

Notes

The weights are used to control the influence that each observation has on the training of the model. ForecasterRecursiveMultiSeries accepts two types of weights. If the two types of weights are indicated, they are multiplied to create the final weights. The resulting sample_weight cannot have negative values.

• series_weights : controls the relative importance of each series. If a series has twice as much weight as the others, the observations of that series influence the training twice as much. The higher the weight of a series relative to the others, the more the model will focus on trying to learn that series.
• weight_func : controls the relative importance of each observation according to its index value. For example, a function that assigns a lower weight to certain dates.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def __init__(
    self,
    regressor: object,
    lags: int | list[int] | np.ndarray[int] | range[int] | None = None,
    window_features: object | list[object] | None = None,
    encoding: str | None = 'ordinal',
    transformer_series: object | dict[str, object] | None = None,
    transformer_exog: object | None = None,
    weight_func: Callable | dict[str, Callable] | None = None,
    series_weights: dict[str, float] | None = None,
    differentiation: int | dict[str, int | None] | None = None,
    dropna_from_series: bool = False,
    fit_kwargs: dict[str, object] | None = None,
    binner_kwargs: dict[str, object] | None = None,
    forecaster_id: str | int | None = None
) -> None:

    self.regressor                          = copy(regressor)
    self.encoding                           = encoding
    self.encoder                            = None
    self.encoding_mapping_                  = {}
    self.transformer_series                 = transformer_series
    self.transformer_series_                = None
    self.transformer_exog                   = transformer_exog
    self.weight_func                        = weight_func
    self.weight_func_                       = None
    self.source_code_weight_func            = None
    self.series_weights                     = series_weights
    self.series_weights_                    = None
    self.differentiation                    = differentiation
    self.differentiation_max                = None
    self.differentiator                     = None
    self.differentiator_                    = None
    self.dropna_from_series                 = dropna_from_series
    self.last_window_                       = None
    self.index_type_                        = None
    self.index_freq_                        = None
    self.training_range_                    = None
    self.series_names_in_                   = None
    self.exog_in_                           = False
    self.exog_names_in_                     = None
    self.exog_type_in_                      = None
    self.exog_dtypes_in_                    = None 
    self.X_train_series_names_in_           = None
    self.X_train_window_features_names_out_ = None
    self.X_train_exog_names_out_            = None
    self.X_train_features_names_out_        = None
    self.in_sample_residuals_               = None
    self.in_sample_residuals_by_bin_        = None
    self.out_sample_residuals_              = None
    self.out_sample_residuals_by_bin_       = None
    self.creation_date                      = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.is_fitted                          = False
    self.fit_date                           = None
    self.skforecast_version                 = skforecast.__version__
    self.python_version                     = sys.version.split(" ")[0]
    self.forecaster_id                      = forecaster_id
    self._probabilistic_mode                = "binned"

    self.lags, self.lags_names, self.max_lag = initialize_lags(type(self).__name__, lags)
    self.window_features, self.window_features_names, self.max_size_window_features = (
        initialize_window_features(window_features)
    )
    if self.window_features is None and self.lags is None:
        raise ValueError(
            "At least one of the arguments `lags` or `window_features` "
            "must be different from None. This is required to create the "
            "predictors used in training the forecaster."
        )

    self.window_size = max(
        [ws for ws in [self.max_lag, self.max_size_window_features] 
         if ws is not None]
    )
    self.window_features_class_names = None
    if window_features is not None:
        self.window_features_class_names = [
            type(wf).__name__ for wf in self.window_features
        ]

    if self.encoding not in ['ordinal', 'ordinal_category', 'onehot', None]:
        raise ValueError(
            f"Argument `encoding` must be one of the following values: 'ordinal', "
            f"'ordinal_category', 'onehot' or None. Got '{self.encoding}'."
        )

    if self.encoding == 'onehot':
        self.encoder = OneHotEncoder(
                           categories    = 'auto',
                           sparse_output = False,
                           drop          = None,
                           dtype         = int
                       ).set_output(transform='pandas')
    else:
        self.encoder = OrdinalEncoder(
                           categories = 'auto',
                           dtype      = int
                       ).set_output(transform='pandas')

    scaling_regressors = tuple(
        member[1]
        for member in inspect.getmembers(sklearn.linear_model, inspect.isclass)
        + inspect.getmembers(sklearn.svm, inspect.isclass)
    )

    if self.transformer_series is None and isinstance(regressor, scaling_regressors):
        warnings.warn(
            "When using a linear model, it is recommended to use a transformer_series "
            "to ensure all series are in the same scale. You can use, for example, a "
            "`StandardScaler` from sklearn.preprocessing.",
            DataTransformationWarning
        )

    if isinstance(self.transformer_series, dict):
        if self.encoding is None:
            raise TypeError(
                "When `encoding` is None, `transformer_series` must be a single "
                "transformer (not `dict`) as it is applied to all series."
            )
        if '_unknown_level' not in self.transformer_series.keys():
            raise ValueError(
                "If `transformer_series` is a `dict`, a transformer must be "
                "provided to transform series that do not exist during training. "
                "Add the key '_unknown_level' to `transformer_series`. "
                "For example: {'_unknown_level': your_transformer}."
            )

    self.weight_func, self.source_code_weight_func, self.series_weights = (
        initialize_weights(
            forecaster_name = type(self).__name__,
            regressor       = regressor,
            weight_func     = weight_func,
            series_weights  = series_weights,
        )
    )

    if differentiation is not None:
        if isinstance(differentiation, int):
            if differentiation < 1:
                raise ValueError(
                    f"If `differentiation` is an integer, it must be equal "
                    f"to or greater than 1. Got {differentiation}."
                )
            self.differentiation = differentiation
            self.differentiation_max = differentiation
            self.window_size += self.differentiation_max
            self.differentiator = TimeSeriesDifferentiator(
                order=differentiation, window_size=self.window_size
            )
        elif isinstance(differentiation, dict):

            if self.encoding is None:
                raise TypeError(
                    "When `encoding` is None, `differentiation` must be an "
                    "integer equal to or greater than 1. Same differentiation "
                    "must be applied to all series."
                )
            if '_unknown_level' not in differentiation.keys():
                raise ValueError(
                    "If `differentiation` is a `dict`, an order must be provided "
                    "to differentiate series that do not exist during training. "
                    "Add the key '_unknown_level' to `differentiation`. "
                    "For example: {'_unknown_level': 1}."
                )

            differentiation_max = []
            for level, diff in differentiation.items():
                if diff is not None:
                    if not isinstance(diff, int) or diff < 1:
                        raise ValueError(
                            f"If `differentiation` is a dict, the values must be "
                            f"None or integers equal to or greater than 1. "
                            f"Got {diff} for series '{level}'."
                        )
                    differentiation_max.append(diff)

            if len(differentiation_max) == 0:
                raise ValueError(
                    "If `differentiation` is a dict, at least one value must be "
                    "different from None. Got all values equal to None. If you "
                    "do not want to differentiate any series, set `differentiation` "
                    "to None."
                )

            self.differentiation = differentiation
            self.differentiation_max = max(differentiation_max)
            self.window_size += self.differentiation_max
            self.differentiator = {
                level: (
                    TimeSeriesDifferentiator(order=diff, window_size=self.window_size)
                    if diff is not None else None
                )
                for level, diff in differentiation.items()
            }
        else:
            raise TypeError(
                f"When including `differentiation`, this argument must be "
                f"an integer (equal to or greater than 1) or a dict of "
                f"integers. Got {type(differentiation)}."
            )

    self.fit_kwargs = check_select_fit_kwargs(
                          regressor  = regressor,
                          fit_kwargs = fit_kwargs
                      )

    self.binner = {}
    self.binner_intervals_ = {}
    self.binner_kwargs = binner_kwargs
    if binner_kwargs is None:
        self.binner_kwargs = {
            'n_bins': 10, 'method': 'linear', 'subsample': 200000,
            'random_state': 789654, 'dtype': np.float64
        }

_repr_html_

_repr_html_()

HTML representation of the object. The "General Information" section is expanded by default.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _repr_html_(self):
    """
    HTML representation of the object.
    The "General Information" section is expanded by default.
    """

    (
        params,
        training_range_,
        series_names_in_,
        exog_names_in_,
        transformer_series,
    ) = self._preprocess_repr(
            regressor          = self.regressor,
            training_range_    = self.training_range_,
            series_names_in_   = self.series_names_in_,
            exog_names_in_     = self.exog_names_in_,
            transformer_series = self.transformer_series,
        )

    style, unique_id = get_style_repr_html(self.is_fitted)

    content = f"""
    <div class="container-{unique_id}">
        <h2>{type(self).__name__}</h2>
        <details open>
            <summary>General Information</summary>
            <ul>
                <li><strong>Regressor:</strong> {type(self.regressor).__name__}</li>
                <li><strong>Lags:</strong> {self.lags}</li>
                <li><strong>Window features:</strong> {self.window_features_names}</li>
                <li><strong>Window size:</strong> {self.window_size}</li>
                <li><strong>Series encoding:</strong> {self.encoding}</li>
                <li><strong>Exogenous included:</strong> {self.exog_in_}</li>
                <li><strong>Weight function included:</strong> {self.weight_func is not None}</li>
                <li><strong>Series weights:</strong> {self.series_weights}</li>
                <li><strong>Differentiation order:</strong> {self.differentiation}</li>
                <li><strong>Creation date:</strong> {self.creation_date}</li>
                <li><strong>Last fit date:</strong> {self.fit_date}</li>
                <li><strong>Skforecast version:</strong> {self.skforecast_version}</li>
                <li><strong>Python version:</strong> {self.python_version}</li>
                <li><strong>Forecaster id:</strong> {self.forecaster_id}</li>
            </ul>
        </details>
        <details>
            <summary>Exogenous Variables</summary>
            <ul>
                {exog_names_in_}
            </ul>
        </details>
        <details>
            <summary>Data Transformations</summary>
            <ul>
                <li><strong>Transformer for series:</strong> {transformer_series}</li>
                <li><strong>Transformer for exog:</strong> {self.transformer_exog}</li>
            </ul>
        </details>
        <details>
            <summary>Training Information</summary>
            <ul>
                <li><strong>Series names (levels):</strong> {series_names_in_}</li>
                <li><strong>Training range:</strong> {training_range_}</li>
                <li><strong>Training index type:</strong> {str(self.index_type_).split('.')[-1][:-2] if self.is_fitted else 'Not fitted'}</li>
                <li><strong>Training index frequency:</strong> {self.index_freq_ if self.is_fitted else 'Not fitted'}</li>
            </ul>
        </details>
        <details>
            <summary>Regressor Parameters</summary>
            <ul>
                {params}
            </ul>
        </details>
        <details>
            <summary>Fit Kwargs</summary>
            <ul>
                {self.fit_kwargs}
            </ul>
        </details>
        <p>
            <a href="https://skforecast.org/{skforecast.__version__}/api/forecasterrecursivemultiseries.html">&#128712 <strong>API Reference</strong></a>
            &nbsp;&nbsp;
            <a href="https://skforecast.org/{skforecast.__version__}/user_guides/independent-multi-time-series-forecasting.html">&#128462 <strong>User Guide</strong></a>
        </p>
    </div>
    """

    return style + content

_create_lags

_create_lags(y, X_as_pandas=False, train_index=None)

Create the lagged values and their target variable from a time series.

Note that the returned matrix X_data contains the lag 1 in the first column, the lag 2 in the in the second column and so on.

Parameters:

Name	Type	Description	Default
y	numpy ndarray	Training time series values.	required
X_as_pandas	bool	If True, the returned matrix X_data is a pandas DataFrame.	False
train_index	pandas Index	Index of the training data. It is used to create the pandas DataFrame X_data when X_as_pandas is True.	None

Returns:

Name	Type	Description
X_data	numpy ndarray, pandas DataFrame, None	Lagged values (predictors).
y_data	numpy ndarray	Values of the time series related to each row of X_data.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_lags(
    self,
    y: np.ndarray,
    X_as_pandas: bool = False,
    train_index: pd.Index | None = None
) -> tuple[np.ndarray | pd.DataFrame | None, np.ndarray]:
    """
    Create the lagged values and their target variable from a time series.

    Note that the returned matrix `X_data` contains the lag 1 in the first 
    column, the lag 2 in the in the second column and so on.

    Parameters
    ----------
    y : numpy ndarray
        Training time series values.
    X_as_pandas : bool, default False
        If `True`, the returned matrix `X_data` is a pandas DataFrame.
    train_index : pandas Index, default None
        Index of the training data. It is used to create the pandas DataFrame
        `X_data` when `X_as_pandas` is `True`.

    Returns
    -------
    X_data : numpy ndarray, pandas DataFrame, None
        Lagged values (predictors).
    y_data : numpy ndarray
        Values of the time series related to each row of `X_data`.

    """

    X_data = None
    if self.lags is not None:
        n_rows = len(y) - self.window_size
        X_data = np.full(
            shape=(n_rows, len(self.lags)), fill_value=np.nan, order='F', dtype=float
        )
        for i, lag in enumerate(self.lags):
            X_data[:, i] = y[self.window_size - lag: -lag]

        if X_as_pandas:
            X_data = pd.DataFrame(
                         data    = X_data,
                         columns = self.lags_names,
                         index   = train_index
                     )

    y_data = y[self.window_size:]

    return X_data, y_data

_create_window_features

_create_window_features(y, train_index, X_as_pandas=False)

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
train_index	pandas Index	Index of the training data. It is used to create the pandas DataFrame X_train_window_features when X_as_pandas is True.	required
X_as_pandas	bool	If True, the returned matrix X_train_window_features is a pandas DataFrame.	False

Returns:

Name	Type	Description
X_train_window_features	list	List of numpy ndarrays or pandas DataFrames with the window features.
X_train_window_features_names_out_	list	Names of the window features.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_window_features(
    self, 
    y: pd.Series,
    train_index: pd.Index,
    X_as_pandas: bool = False,
) -> tuple[list[np.ndarray | pd.DataFrame], list[str]]:
    """

    Parameters
    ----------
    y : pandas Series
        Training time series.
    train_index : pandas Index
        Index of the training data. It is used to create the pandas DataFrame
        `X_train_window_features` when `X_as_pandas` is `True`.
    X_as_pandas : bool, default False
        If `True`, the returned matrix `X_train_window_features` is a 
        pandas DataFrame.

    Returns
    -------
    X_train_window_features : list
        List of numpy ndarrays or pandas DataFrames with the window features.
    X_train_window_features_names_out_ : list
        Names of the window features.

    """

    len_train_index = len(train_index)
    X_train_window_features = []
    X_train_window_features_names_out_ = []
    for wf in self.window_features:
        X_train_wf = wf.transform_batch(y)
        if not isinstance(X_train_wf, pd.DataFrame):
            raise TypeError(
                f"The method `transform_batch` of {type(wf).__name__} "
                f"must return a pandas DataFrame."
            )
        X_train_wf = X_train_wf.iloc[-len_train_index:]
        if not len(X_train_wf) == len_train_index:
            raise ValueError(
                f"The method `transform_batch` of {type(wf).__name__} "
                f"must return a DataFrame with the same number of rows as "
                f"the input time series - `window_size`: {len_train_index}."
            )
        if not (X_train_wf.index == train_index).all():
            raise ValueError(
                f"The method `transform_batch` of {type(wf).__name__} "
                f"must return a DataFrame with the same index as "
                f"the input time series - `window_size`."
            )

        X_train_window_features_names_out_.extend(X_train_wf.columns)
        if not X_as_pandas:
            X_train_wf = X_train_wf.to_numpy()     
        X_train_window_features.append(X_train_wf)

    return X_train_window_features, X_train_window_features_names_out_

_create_train_X_y_single_series

_create_train_X_y_single_series(y, ignore_exog, exog=None)

Create training matrices from univariate time series and exogenous variables. This method does not transform the exog variables.

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
ignore_exog	bool	If True, exog is ignored.	required
exog	pandas DataFrame	Exogenous variable/s included as predictor/s.	None

Returns:

Name	Type	Description
X_train_lags	pandas DataFrame	Training values of lags. Shape: (len(y) - self.max_lag, len(self.lags))
X_train_window_features_names_out_	list	Names of the window features.
X_train_exog	pandas DataFrame	Training values of exogenous variables. Shape: (len(y) - self.max_lag, len(exog.columns))
y_train	pandas Series	Values (target) of the time series related to each row of X_train. Shape: (len(y) - self.max_lag, )

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_train_X_y_single_series(
    self,
    y: pd.Series,
    ignore_exog: bool,
    exog: pd.DataFrame | None = None
) -> tuple[pd.DataFrame, list[str], pd.DataFrame, pd.Series]:
    """
    Create training matrices from univariate time series and exogenous
    variables. This method does not transform the exog variables.

    Parameters
    ----------
    y : pandas Series
        Training time series.
    ignore_exog : bool
        If `True`, `exog` is ignored.
    exog : pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.

    Returns
    -------
    X_train_lags : pandas DataFrame
        Training values of lags.
        Shape: (len(y) - self.max_lag, len(self.lags))
    X_train_window_features_names_out_ : list
        Names of the window features.
    X_train_exog : pandas DataFrame
        Training values of exogenous variables.
        Shape: (len(y) - self.max_lag, len(exog.columns))
    y_train : pandas Series
        Values (target) of the time series related to each row of `X_train`.
        Shape: (len(y) - self.max_lag, )

    """

    series_name = y.name
    if len(y) <= self.window_size:
        raise ValueError(
            f"Length of '{series_name}' must be greater than the maximum window size "
            f"needed by the forecaster.\n"
            f"    Length '{series_name}': {len(y)}.\n"
            f"    Max window size: {self.window_size}.\n"
            f"    Lags window size: {self.max_lag}.\n"
            f"    Window features window size: {self.max_size_window_features}."
        )

    if self.encoding is None:
        fit_transformer = False
        transformer_series = self.transformer_series_['_unknown_level']
    else:
        fit_transformer = False if self.is_fitted else True
        transformer_series = self.transformer_series_[series_name]

    y = transform_series(
            series            = y,
            transformer       = transformer_series,
            fit               = fit_transformer,
            inverse_transform = False
        )

    y_values = y.to_numpy()
    y_index = y.index

    if self.differentiator_[series_name] is not None:
        if not self.is_fitted:
            y_values = self.differentiator_[series_name].fit_transform(y_values)
        else:
            differentiator = copy(self.differentiator_[series_name])
            y_values = differentiator.fit_transform(y_values)

    X_train_autoreg = []
    train_index = y_index[self.window_size:]

    X_train_lags, y_train = self._create_lags(
        y=y_values, X_as_pandas=True, train_index=train_index
    )
    if X_train_lags is not None:
        X_train_autoreg.append(X_train_lags)

    X_train_window_features_names_out_ = None
    if self.window_features is not None:
        # NOTE: The first `self.differentiation_max` positions of `y_values`
        # must be removed to match the length of `y_train` after creating
        # the window features. This is because `y_train` is created using the 
        # global window size of the Forecaster, which includes the maximum 
        # differentiation (self.differentiation_max).
        n_diff = 0 if self.differentiation is None else self.differentiation_max
        y_window_features = pd.Series(y_values[n_diff:], index=y_index[n_diff:])
        X_train_window_features, X_train_window_features_names_out_ = (
            self._create_window_features(
                y=y_window_features, X_as_pandas=True, train_index=train_index
            )
        )
        X_train_autoreg.extend(X_train_window_features)

    if len(X_train_autoreg) == 1:
        X_train_autoreg = X_train_autoreg[0]
    else:
        X_train_autoreg = pd.concat(X_train_autoreg, axis=1)

    X_train_autoreg['_level_skforecast'] = series_name

    if ignore_exog:
        X_train_exog = None
    else:
        if exog is not None:
            # The first `self.window_size` positions have to be removed from exog
            # since they are not in X_train_autoreg.
            X_train_exog = exog.iloc[self.window_size:, ]
        else:
            X_train_exog = pd.DataFrame(
                               data    = np.nan,
                               columns = ['_dummy_exog_col_to_keep_shape'],
                               index   = train_index
                           )

    y_train = pd.Series(
                  data  = y_train,
                  index = train_index,
                  name  = 'y'
              )

    return X_train_autoreg, X_train_window_features_names_out_, X_train_exog, y_train

_create_train_X_y

_create_train_X_y(
    series, exog=None, store_last_window=True
)

Create training matrices from multiple time series and exogenous variables. See Notes section for more details depending on the type of series and exog.

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
store_last_window	(bool, list)	Whether or not to store the last window (last_window_) of training data. If True, last window is stored for all series. If list, last window is stored for the series present in the list. If False, last window is not stored.	True

Returns:

Name	Type	Description
X_train	pandas DataFrame	Training values (predictors).
y_train	pandas Series	Values of the time series related to each row of X_train.
series_indexes	dict	Dictionary with the index of each series.
series_names_in_	list	Names of the series (levels) provided by the user during training.
X_train_series_names_in_	list	Names of the series (levels) included in the matrix X_train created internally for training. It can be different from series_names_in_ if some series are dropped during the training process because of NaNs or because they are not present in the training period.
exog_names_in_	list	Names of the exogenous variables used during training.
X_train_window_features_names_out_	list	Names of the window features included in the matrix X_train created internally for training.
X_train_exog_names_out_	list	Names of the exogenous variables included in the matrix X_train created internally for training. It can be different from exog_names_in_ if some exogenous variables are transformed during the training process.
exog_dtypes_in_	dict	Type of each exogenous variable/s used in training. If transformer_exog is used, the dtypes are calculated before the transformation.
last_window_	dict	Last window of training data for each series. It stores the values needed to predict the next step immediately after the training data.

Notes

• If series is a pandas DataFrame and exog is a pandas Series or DataFrame, each exog is duplicated for each series. Exog must have the same index as series (type, length and frequency).
• If series is a pandas DataFrame and exog is a dict of pandas Series or DataFrames. Each key in exog must be a column in series and the values are the exog for each series. Exog must have the same index as series (type, length and frequency).
• If series is a dict of pandas Series, exog must be a dict of pandas Series or DataFrames. The keys in series and exog must be the same. All series and exog must have a pandas DatetimeIndex with the same frequency.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_train_X_y(
    self,
    series: pd.DataFrame | dict[str, pd.Series | pd.DataFrame],
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    store_last_window: bool | list[str] = True,
) -> tuple[
    pd.DataFrame,
    pd.Series,
    dict[str, pd.Index],
    list[str],
    list[str],
    list[str],
    list[str],
    list[str],
    dict[str, type],
    dict[str, pd.Series],
]:
    """
    Create training matrices from multiple time series and exogenous
    variables. See Notes section for more details depending on the type of
    `series` and `exog`.

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    store_last_window : bool, list, default True
        Whether or not to store the last window (`last_window_`) of training data.

        - If `True`, last window is stored for all series. 
        - If `list`, last window is stored for the series present in the list.
        - If `False`, last window is not stored.

    Returns
    -------
    X_train : pandas DataFrame
        Training values (predictors).
    y_train : pandas Series
        Values of the time series related to each row of `X_train`.
    series_indexes : dict
        Dictionary with the index of each series.
    series_names_in_ : list
        Names of the series (levels) provided by the user during training.
    X_train_series_names_in_ : list
        Names of the series (levels) included in the matrix `X_train` created
        internally for training. It can be different from `series_names_in_` if
        some series are dropped during the training process because of NaNs or
        because they are not present in the training period.
    exog_names_in_ : list
        Names of the exogenous variables used during training.
    X_train_window_features_names_out_ : list
        Names of the window features included in the matrix `X_train` created
        internally for training.
    X_train_exog_names_out_ : list
        Names of the exogenous variables included in the matrix `X_train` created
        internally for training. It can be different from `exog_names_in_` if
        some exogenous variables are transformed during the training process.
    exog_dtypes_in_ : dict
        Type of each exogenous variable/s used in training. If `transformer_exog` 
        is used, the dtypes are calculated before the transformation.
    last_window_ : dict
        Last window of training data for each series. It stores the values 
        needed to predict the next `step` immediately after the training data.

    Notes
    -----
    - If `series` is a pandas DataFrame and `exog` is a pandas Series or 
    DataFrame, each exog is duplicated for each series. Exog must have the
    same index as `series` (type, length and frequency).
    - If `series` is a pandas DataFrame and `exog` is a dict of pandas Series 
    or DataFrames. Each key in `exog` must be a column in `series` and the 
    values are the exog for each series. Exog must have the same index as 
    `series` (type, length and frequency).
    - If `series` is a dict of pandas Series, `exog` must be a dict of pandas
    Series or DataFrames. The keys in `series` and `exog` must be the same.
    All series and exog must have a pandas DatetimeIndex with the same 
    frequency.

    """

    series_dict, series_indexes = check_preprocess_series(series=series)
    input_series_is_dict = isinstance(series, dict)
    series_names_in_ = list(series_dict.keys())

    if self.is_fitted and not set(series_names_in_).issubset(set(self.series_names_in_)):
        raise ValueError(
            f"Once the Forecaster has been trained, `series` must contain "
            f"the same series names as those used during training:\n"
            f" Got      : {series_names_in_}\n"
            f" Expected : {self.series_names_in_}"
        )

    exog_dict = {serie: None for serie in series_names_in_}
    exog_names_in_ = None
    X_train_exog_names_out_ = None
    if exog is not None:
        exog_dict, exog_names_in_ = check_preprocess_exog_multiseries(
                                        input_series_is_dict = input_series_is_dict,
                                        series_indexes       = series_indexes,
                                        series_names_in_     = series_names_in_,
                                        exog                 = exog,
                                        exog_dict            = exog_dict
                                    )

        if self.is_fitted:
            if self.exog_names_in_ is None:
                raise ValueError(
                    "Once the Forecaster has been trained, `exog` must be `None` "
                    "because no exogenous variables were added during training."
                )
            else:
                if not set(exog_names_in_) == set(self.exog_names_in_):
                    raise ValueError(
                        f"Once the Forecaster has been trained, `exog` must contain "
                        f"the same exogenous variables as those used during training:\n"
                        f" Got      : {exog_names_in_}\n"
                        f" Expected : {self.exog_names_in_}"
                    )

    if not self.is_fitted:
        self.transformer_series_ = initialize_transformer_series(
                                       forecaster_name    = type(self).__name__,
                                       series_names_in_   = series_names_in_,
                                       encoding           = self.encoding,
                                       transformer_series = self.transformer_series
                                   )

        self.differentiator_ = initialize_differentiator_multiseries(
                                   series_names_in_ = series_names_in_,
                                   differentiator   = self.differentiator
                               )

    series_dict, exog_dict = align_series_and_exog_multiseries(
                                 series_dict          = series_dict,
                                 input_series_is_dict = input_series_is_dict,
                                 exog_dict            = exog_dict
                             )

    if not self.is_fitted and self.transformer_series_['_unknown_level'] is not None:
        self.transformer_series_['_unknown_level'].fit(
            np.concatenate(list(series_dict.values())).reshape(-1, 1)
        )

    ignore_exog = True if exog is None else False
    input_matrices = [
        [series_dict[k], exog_dict[k], ignore_exog]
         for k in series_dict.keys()
    ]

    X_train_autoreg_buffer = []
    X_train_exog_buffer = []
    y_train_buffer = []
    for matrices in input_matrices:

        (
            X_train_autoreg,
            X_train_window_features_names_out_,
            X_train_exog,
            y_train
        ) = self._create_train_X_y_single_series(
            y           = matrices[0],
            exog        = matrices[1],
            ignore_exog = matrices[2],
        )

        X_train_autoreg_buffer.append(X_train_autoreg)
        X_train_exog_buffer.append(X_train_exog)
        y_train_buffer.append(y_train)

    X_train = pd.concat(X_train_autoreg_buffer, axis=0)
    y_train = pd.concat(y_train_buffer, axis=0)

    if self.is_fitted:
        encoded_values = self.encoder.transform(X_train[['_level_skforecast']])
    else:
        encoded_values = self.encoder.fit_transform(X_train[['_level_skforecast']])
        for i, code in enumerate(self.encoder.categories_[0]):
            self.encoding_mapping_[code] = i

    X_train = pd.concat([
                  X_train.drop(columns='_level_skforecast'),
                  encoded_values
              ], axis=1)

    if self.encoding == 'onehot':
        X_train.columns = X_train.columns.str.replace('_level_skforecast_', '')
    elif self.encoding == 'ordinal_category':
        X_train['_level_skforecast'] = (
            X_train['_level_skforecast'].astype('category')
        )

    del encoded_values

    exog_dtypes_in_ = None
    if exog is not None:

        X_train_exog = pd.concat(X_train_exog_buffer, axis=0)
        if '_dummy_exog_col_to_keep_shape' in X_train_exog.columns:
            X_train_exog = (
                X_train_exog.drop(columns=['_dummy_exog_col_to_keep_shape'])
            )

        exog_names_in_ = X_train_exog.columns.to_list()
        exog_dtypes_in_ = get_exog_dtypes(exog=X_train_exog)

        fit_transformer = False if self.is_fitted else True
        X_train_exog = transform_dataframe(
                           df                = X_train_exog,
                           transformer       = self.transformer_exog,
                           fit               = fit_transformer,
                           inverse_transform = False
                       )

        check_exog_dtypes(X_train_exog, call_check_exog=False)
        if not (X_train_exog.index == X_train.index).all():
            raise ValueError(
                "Different index for `series` and `exog` after transformation. "
                "They must be equal to ensure the correct alignment of values."
            )

        X_train_exog_names_out_ = X_train_exog.columns.to_list()
        X_train = pd.concat([X_train, X_train_exog], axis=1)

    if y_train.isnull().any():
        mask = y_train.notna().to_numpy()
        y_train = y_train.iloc[mask]
        X_train = X_train.iloc[mask,]
        warnings.warn(
            "NaNs detected in `y_train`. They have been dropped because the "
            "target variable cannot have NaN values. Same rows have been "
            "dropped from `X_train` to maintain alignment. This is caused by "
            "series with interspersed NaNs.",
            MissingValuesWarning
        )

    if self.dropna_from_series:
        if np.any(X_train.isnull().to_numpy()):
            mask = X_train.notna().all(axis=1).to_numpy()
            X_train = X_train.iloc[mask, ]
            y_train = y_train.iloc[mask]
            warnings.warn(
                "NaNs detected in `X_train`. They have been dropped. If "
                "you want to keep them, set `forecaster.dropna_from_series = False`. "
                "Same rows have been removed from `y_train` to maintain alignment. "
                "This caused by series with interspersed NaNs.",
                MissingValuesWarning
            )
    else:
        if np.any(X_train.isnull().to_numpy()):
            warnings.warn(
                "NaNs detected in `X_train`. Some regressors do not allow "
                "NaN values during training. If you want to drop them, "
                "set `forecaster.dropna_from_series = True`.",
                MissingValuesWarning
            )

    if X_train.empty:
        raise ValueError(
            "All samples have been removed due to NaNs. Set "
            "`forecaster.dropna_from_series = False` or review `exog` values."
        )

    if self.encoding == 'onehot':
        X_train_series_names_in_ = [
            col for col in series_names_in_ if X_train[col].sum() > 0
        ]
    else:
        unique_levels = X_train['_level_skforecast'].unique()
        X_train_series_names_in_ = [
            k for k, v in self.encoding_mapping_.items()
            if v in unique_levels
        ]

    # The last time window of training data is stored so that lags needed as
    # predictors in the first iteration of `predict()` can be calculated.
    last_window_ = None
    if store_last_window:

        series_to_store = (
            X_train_series_names_in_ if store_last_window is True else store_last_window
        )

        series_not_in_series_dict = set(series_to_store) - set(X_train_series_names_in_)
        if series_not_in_series_dict:
            warnings.warn(
                f"Series {series_not_in_series_dict} are not present in "
                f"`series`. No last window is stored for them.",
                IgnoredArgumentWarning
            )
            series_to_store = [
                s for s in series_to_store 
                if s not in series_not_in_series_dict
            ]

        if series_to_store:
            last_window_ = {
                k: v.iloc[-self.window_size:].copy()
                for k, v in series_dict.items()
                if k in series_to_store
            }

    return (
        X_train,
        y_train,
        series_indexes,
        series_names_in_,
        X_train_series_names_in_,
        exog_names_in_,
        X_train_window_features_names_out_,
        X_train_exog_names_out_,
        exog_dtypes_in_,
        last_window_
    )

create_train_X_y

create_train_X_y(
    series, exog=None, suppress_warnings=False
)

Create training matrices from multiple time series and exogenous variables. See Notes section for more details depending on the type of series and exog.

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the creation of the training matrices. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
X_train	pandas DataFrame	Training values (predictors).
y_train	pandas Series	Values (target) of the time series related to each row of X_train.

Notes

• If series is a pandas DataFrame and exog is a pandas Series or DataFrame, each exog is duplicated for each series. Exog must have the same index as series (type, length and frequency).
• If series is a pandas DataFrame and exog is a dict of pandas Series or DataFrames. Each key in exog must be a column in series and the values are the exog for each series. Exog must have the same index as series (type, length and frequency).
• If series is a dict of pandas Series, exog must be a dict of pandas Series or DataFrames. The keys in series and exog must be the same. All series and exog must have a pandas DatetimeIndex with the same frequency.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def create_train_X_y(
    self,
    series: pd.DataFrame | dict[str, pd.Series | pd.DataFrame],
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    suppress_warnings: bool = False
) -> tuple[pd.DataFrame, pd.Series]:
    """
    Create training matrices from multiple time series and exogenous
    variables. See Notes section for more details depending on the type of
    `series` and `exog`.

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the creation
        of the training matrices. See skforecast.exceptions.warn_skforecast_categories 
        for more information.

    Returns
    -------
    X_train : pandas DataFrame
        Training values (predictors).
    y_train : pandas Series
        Values (target) of the time series related to each row of `X_train`.

    Notes
    -----
    - If `series` is a pandas DataFrame and `exog` is a pandas Series or 
    DataFrame, each exog is duplicated for each series. Exog must have the
    same index as `series` (type, length and frequency).
    - If `series` is a pandas DataFrame and `exog` is a dict of pandas Series 
    or DataFrames. Each key in `exog` must be a column in `series` and the 
    values are the exog for each series. Exog must have the same index as 
    `series` (type, length and frequency).
    - If `series` is a dict of pandas Series, `exog` must be a dict of pandas
    Series or DataFrames. The keys in `series` and `exog` must be the same.
    All series and exog must have a pandas DatetimeIndex with the same 
    frequency.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    output = self._create_train_X_y(
                 series            = series, 
                 exog              = exog, 
                 store_last_window = False
             )

    X_train = output[0]
    y_train = output[1]

    if self.encoding is None:
        X_train = X_train.drop(columns='_level_skforecast')

    set_skforecast_warnings(suppress_warnings, action='default')

    return X_train, y_train

_train_test_split_one_step_ahead

_train_test_split_one_step_ahead(
    series, initial_train_size, exog=None
)

Create matrices needed to train and test the forecaster for one-step-ahead predictions.

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
initial_train_size	int	Initial size of the training set. It is the number of observations used to train the forecaster before making the first prediction.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None

Returns:

Name	Type	Description
X_train	pandas DataFrame	Predictor values used to train the model.
y_train	pandas Series	Target values related to each row of X_train.
X_test	pandas DataFrame	Predictor values used to test the model.
y_test	pandas Series	Target values related to each row of X_test.
X_train_encoding	pandas Series	Series identifiers for each row of X_train.
X_test_encoding	pandas Series	Series identifiers for each row of X_test.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _train_test_split_one_step_ahead(
    self,
    series: pd.DataFrame | dict[str, pd.Series | pd.DataFrame],
    initial_train_size: int,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None
) -> tuple[pd.DataFrame, pd.Series, pd.DataFrame, pd.Series, pd.Series, pd.Series]:
    """
    Create matrices needed to train and test the forecaster for one-step-ahead
    predictions.

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    initial_train_size : int
        Initial size of the training set. It is the number of observations used
        to train the forecaster before making the first prediction.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.

    Returns
    -------
    X_train : pandas DataFrame
        Predictor values used to train the model.
    y_train : pandas Series
        Target values related to each row of `X_train`.
    X_test : pandas DataFrame
        Predictor values used to test the model.
    y_test : pandas Series
        Target values related to each row of `X_test`.
    X_train_encoding : pandas Series
        Series identifiers for each row of `X_train`.
    X_test_encoding : pandas Series
        Series identifiers for each row of `X_test`.

    """

    if isinstance(series, dict):
        freqs = [s.index.freq for s in series.values() if s.index.freq is not None]
        if not freqs:
            raise ValueError("At least one series must have a frequency.")
        if not all(f == freqs[0] for f in freqs):
            raise ValueError(
                "All series with frequency must have the same frequency."
            )

        min_index = min([v.index[0] for v in series.values() if not v.empty])
        max_index = max([v.index[-1] for v in series.values() if not v.empty])
        span_index = pd.date_range(start=min_index, end=max_index, freq=freqs[0])
    else:
        span_index = series.index

    fold = [
        [0, initial_train_size],
        [initial_train_size - self.window_size, initial_train_size],
        [initial_train_size - self.window_size, len(span_index)],
        [0, 0],  # Dummy value
        True
    ]
    data_fold = _extract_data_folds_multiseries(
                    series             = series,
                    folds              = [fold],
                    span_index         = span_index,
                    window_size        = self.window_size,
                    exog               = exog,
                    dropna_last_window = self.dropna_from_series,
                    externally_fitted  = False
                )
    series_train, _, levels_last_window, exog_train, exog_test, _ = next(data_fold)

    start_test_idx = initial_train_size - self.window_size
    if isinstance(series, pd.DataFrame):
        series_test = series.iloc[start_test_idx:, :]
        series_test = series_test.loc[:, levels_last_window]
        series_test = series_test.dropna(axis=1, how='all')
    elif isinstance(series, dict):
        start_test_date = span_index[start_test_idx]
        series_test = {
            k: v.loc[v.index >= start_test_date]
            for k, v in series.items()
            if k in levels_last_window and not v.empty and not v.isna().all()
        }

    _is_fitted = self.is_fitted
    _series_names_in_ = self.series_names_in_
    _exog_names_in_ = self.exog_names_in_

    self.is_fitted = False
    X_train, y_train, _, series_names_in_, _, exog_names_in_, *_ = (
        self._create_train_X_y(
            series            = series_train,
            exog              = exog_train,
            store_last_window = False
        )
    )

    self.series_names_in_ = series_names_in_
    if exog is not None:
        self.exog_names_in_ = exog_names_in_
    self.is_fitted = True

    X_test, y_test, *_ = self._create_train_X_y(
                             series            = series_test,
                             exog              = exog_test,
                             store_last_window = False
                         )
    self.is_fitted = _is_fitted
    self.series_names_in_ = _series_names_in_
    self.exog_names_in_ = _exog_names_in_

    if self.encoding in ["ordinal", "ordinal_category"]:
        X_train_encoding = self.encoder.inverse_transform(
            X_train[["_level_skforecast"]]
        ).ravel()
        X_test_encoding = self.encoder.inverse_transform(
            X_test[["_level_skforecast"]]
        ).ravel()
    elif self.encoding == 'onehot':
        X_train_encoding = self.encoder.inverse_transform(
            X_train.loc[:, self.encoding_mapping_.keys()]
        ).ravel()
        X_test_encoding = self.encoder.inverse_transform(
            X_test.loc[:, self.encoding_mapping_.keys()]
        ).ravel()
    else:
        X_train_encoding = self.encoder.inverse_transform(
            X_train[["_level_skforecast"]]
        ).ravel()
        X_test_encoding = self.encoder.inverse_transform(
            X_test[["_level_skforecast"]]
        ).ravel()
        X_train = X_train.drop(columns="_level_skforecast")
        X_test = X_test.drop(columns="_level_skforecast")

    X_train_encoding = pd.Series(
        data=X_train_encoding, index=X_train.index
    ).fillna("_unknown_level")
    X_test_encoding = pd.Series(
        data=X_test_encoding, index=X_test.index
    ).fillna("_unknown_level")

    return X_train, y_train, X_test, y_test, X_train_encoding, X_test_encoding

_weight_func_all_1

_weight_func_all_1(index)

Weight function that assigns a weight of 1 to all observations.

Parameters:

Name	Type	Description	Default
index	pandas Index	Index of the series.	required

Returns:

Name	Type	Description
weights	numpy ndarray	Weights to use in fit method.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _weight_func_all_1(
    self, 
    index: pd.Index
) -> np.ndarray:
    """
    Weight function that assigns a weight of 1 to all observations.

    Parameters
    ----------
    index : pandas Index
        Index of the series.

    Returns
    -------
    weights : numpy ndarray
        Weights to use in `fit` method.

    """

    weights = np.ones(len(index), dtype=float)

    return weights

create_sample_weights

create_sample_weights(series_names_in_, X_train)

Create weights for each observation according to the forecaster's attributes series_weights and weight_func. The resulting weights are product of both types of weights.

Parameters:

Name	Type	Description	Default
series_names_in_	list	Names of the series (levels) used during training.	required
X_train	pandas DataFrame	Dataframe created with the create_train_X_y method, first return.	required

Returns:

Name	Type	Description
weights	numpy ndarray	Weights to use in fit method.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def create_sample_weights(
    self,
    series_names_in_: list,
    X_train: pd.DataFrame
) -> np.ndarray:
    """
    Create weights for each observation according to the forecaster's attributes
    `series_weights` and `weight_func`. The resulting weights are product of both
    types of weights.

    Parameters
    ----------
    series_names_in_ : list
        Names of the series (levels) used during training.
    X_train : pandas DataFrame
        Dataframe created with the `create_train_X_y` method, first return.

    Returns
    -------
    weights : numpy ndarray
        Weights to use in `fit` method.

    """

    weights = None
    weights_samples = None
    series_weights = None

    if self.series_weights is not None:
        # Series not present in series_weights have a weight of 1 in all their samples.
        # Keys in series_weights not present in series are ignored.
        series_not_in_series_weights = (
            set(series_names_in_) - set(self.series_weights.keys())
        )
        if series_not_in_series_weights:
            warnings.warn(
                f"{series_not_in_series_weights} not present in `series_weights`. "
                f"A weight of 1 is given to all their samples.",
                IgnoredArgumentWarning
            )
        self.series_weights_ = {col: 1. for col in series_names_in_}
        self.series_weights_.update(
            {
                k: v
                for k, v in self.series_weights.items()
                if k in self.series_weights_
            }
        )

        if self.encoding == "onehot":
            series_weights = [
                np.repeat(self.series_weights_[serie], sum(X_train[serie]))
                for serie in series_names_in_
            ]
        else:
            series_weights = [
                np.repeat(
                    self.series_weights_[serie],
                    sum(X_train["_level_skforecast"] == self.encoding_mapping_[serie]),
                )
                for serie in series_names_in_
            ]

        series_weights = np.concatenate(series_weights)

    if self.weight_func is not None:
        if isinstance(self.weight_func, Callable):
            self.weight_func_ = {col: copy(self.weight_func)
                                 for col in series_names_in_}
        else:
            # Series not present in weight_func have a weight of 1 in all their samples
            series_not_in_weight_func = (
                set(series_names_in_) - set(self.weight_func.keys())
            )
            if series_not_in_weight_func:
                warnings.warn(
                    f"{series_not_in_weight_func} not present in `weight_func`. "
                    f"A weight of 1 is given to all their samples.",
                    IgnoredArgumentWarning
                )
            self.weight_func_ = {
                col: self._weight_func_all_1 for col in series_names_in_
            }
            self.weight_func_.update(
                {
                    k: v
                    for k, v in self.weight_func.items()
                    if k in self.weight_func_
                }
            )

        weights_samples = []
        for key in self.weight_func_.keys():
            if self.encoding == "onehot":
                idx = X_train.index[X_train[key] == 1.0]
            else:
                idx = X_train.index[
                    X_train["_level_skforecast"] == self.encoding_mapping_[key]
                ]
            weights_samples.append(self.weight_func_[key](idx))
        weights_samples = np.concatenate(weights_samples)

    if series_weights is not None:
        weights = series_weights
        if weights_samples is not None:
            weights = weights * weights_samples
    else:
        if weights_samples is not None:
            weights = weights_samples

    if weights is not None:
        if np.isnan(weights).any():
            raise ValueError(
                "The resulting `weights` cannot have NaN values."
            )
        if np.any(weights < 0):
            raise ValueError(
                "The resulting `weights` cannot have negative values."
            )
        if np.sum(weights) == 0:
            raise ValueError(
                "The resulting `weights` cannot be normalized because "
                "the sum of the weights is zero."
            )

    return weights

fit

fit(
    series,
    exog=None,
    store_last_window=True,
    store_in_sample_residuals=False,
    random_state=123,
    suppress_warnings=False,
)

Training Forecaster. See Notes section for more details depending on the type of series and exog.

Additional arguments to be passed to the fit method of the regressor can be added with the fit_kwargs argument when initializing the forecaster.

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
store_last_window	(bool, list)	Whether or not to store the last window (last_window_) of training data. If True, last window is stored for all series. If list, last window is stored for the series present in the list. If False, last window is not stored.	True
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting (in_sample_residuals_ and in_sample_residuals_by_bin_ attributes). If False, only the intervals of the bins are stored.	False
random_state	int	Set a seed for the random generator so that the stored sample residuals are always deterministic.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the training process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Type	Description
None

Notes

• If series is a pandas DataFrame and exog is a pandas Series or DataFrame, each exog is duplicated for each series. Exog must have the same index as series (type, length and frequency).
• If series is a pandas DataFrame and exog is a dict of pandas Series or DataFrames. Each key in exog must be a column in series and the values are the exog for each series. Exog must have the same index as series (type, length and frequency).
• If series is a dict of pandas Series, exogmust be a dict of pandas Series or DataFrames. The keys in series and exog must be the same. All series and exog must have a pandas DatetimeIndex with the same frequency.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def fit(
    self,
    series: pd.DataFrame | dict[str, pd.Series | pd.DataFrame],
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    store_last_window: bool | list[str] = True,
    store_in_sample_residuals: bool = False,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> None:
    """
    Training Forecaster. See Notes section for more details depending on 
    the type of `series` and `exog`.

    Additional arguments to be passed to the `fit` method of the regressor 
    can be added with the `fit_kwargs` argument when initializing the forecaster.

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    store_last_window : bool, list, default True
        Whether or not to store the last window (`last_window_`) of training data.

        - If `True`, last window is stored for all series. 
        - If `list`, last window is stored for the series present in the list.
        - If `False`, last window is not stored.
    store_in_sample_residuals : bool, default False
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` and `in_sample_residuals_by_bin_`
        attributes).
        If `False`, only the intervals of the bins are stored.
    random_state : int, default 123
        Set a seed for the random generator so that the stored sample 
        residuals are always deterministic.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the training 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    None

    Notes
    -----
    - If `series` is a pandas DataFrame and `exog` is a pandas Series or 
    DataFrame, each exog is duplicated for each series. Exog must have the
    same index as `series` (type, length and frequency).
    - If `series` is a pandas DataFrame and `exog` is a dict of pandas Series 
    or DataFrames. Each key in `exog` must be a column in `series` and the 
    values are the exog for each series. Exog must have the same index as 
    `series` (type, length and frequency).
    - If `series` is a dict of pandas Series, `exog`must be a dict of pandas
    Series or DataFrames. The keys in `series` and `exog` must be the same.
    All series and exog must have a pandas DatetimeIndex with the same 
    frequency.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    # TODO: create a method reset_forecaster() to reset all attributes
    # Reset values in case the forecaster has already been fitted.
    self.last_window_                       = None
    self.index_type_                        = None
    self.index_freq_                        = None
    self.training_range_                    = None
    self.series_names_in_                   = None
    self.exog_in_                           = False
    self.exog_names_in_                     = None
    self.exog_type_in_                      = None
    self.exog_dtypes_in_                    = None
    self.X_train_series_names_in_           = None
    self.X_train_window_features_names_out_ = None
    self.X_train_exog_names_out_            = None
    self.X_train_features_names_out_        = None
    self.in_sample_residuals_               = None
    self.in_sample_residuals_by_bin_        = None
    self.binner                             = {}
    self.binner_intervals_                  = {}
    self.is_fitted                          = False
    self.fit_date                           = None

    (
        X_train,
        y_train,
        series_indexes,
        series_names_in_,
        X_train_series_names_in_,
        exog_names_in_,
        X_train_window_features_names_out_,
        X_train_exog_names_out_,
        exog_dtypes_in_,
        last_window_
    ) = self._create_train_X_y(
            series=series, exog=exog, store_last_window=store_last_window
        )

    sample_weight = self.create_sample_weights(
                        series_names_in_ = series_names_in_,
                        X_train          = X_train
                    )

    X_train_regressor = (
        X_train
        if self.encoding is not None
        else X_train.drop(columns="_level_skforecast")
    )
    if sample_weight is not None:
        self.regressor.fit(
            X             = X_train_regressor,
            y             = y_train,
            sample_weight = sample_weight,
            **self.fit_kwargs
        )
    else:
        self.regressor.fit(X=X_train_regressor, y=y_train, **self.fit_kwargs)

    self.series_names_in_ = series_names_in_
    self.X_train_series_names_in_ = X_train_series_names_in_
    self.X_train_window_features_names_out_ = X_train_window_features_names_out_
    self.X_train_features_names_out_ = X_train_regressor.columns.to_list()

    self.is_fitted = True
    self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.training_range_ = {k: v[[0, -1]] for k, v in series_indexes.items()}
    self.index_type_ = type(series_indexes[series_names_in_[0]])
    if isinstance(series_indexes[series_names_in_[0]], pd.DatetimeIndex):
        self.index_freq_ = series_indexes[series_names_in_[0]].freqstr
    else:
        self.index_freq_ = series_indexes[series_names_in_[0]].step

    if exog is not None:
        self.exog_in_ = True
        self.exog_names_in_ = exog_names_in_
        self.exog_type_in_ = type(exog)
        self.exog_dtypes_in_ = exog_dtypes_in_
        self.X_train_exog_names_out_ = X_train_exog_names_out_

    self.in_sample_residuals_ = {}
    self.in_sample_residuals_by_bin_ = {}
    if self._probabilistic_mode is not False:
        y_pred = self.regressor.predict(X_train_regressor)
        if self.encoding is not None:
            for level in X_train_series_names_in_:
                if self.encoding == 'onehot':
                    mask = X_train[level].to_numpy() == 1.
                else:
                    encoded_value = self.encoding_mapping_[level]
                    mask = X_train['_level_skforecast'].to_numpy() == encoded_value

                self._binning_in_sample_residuals(
                    level                     = level,
                    y_true                    = y_train[mask],
                    y_pred                    = y_pred[mask],
                    store_in_sample_residuals = store_in_sample_residuals,
                    random_state              = random_state
                )

        # NOTE: the _unknown_level is a random sample of 10_000 residuals of all levels.
        self._binning_in_sample_residuals(
            level                     = '_unknown_level',
            y_true                    = y_train,
            y_pred                    = y_pred,
            store_in_sample_residuals = store_in_sample_residuals,
            random_state              = random_state
        )

    if not store_in_sample_residuals:
        # NOTE: create empty dictionaries to avoid errors when calling predict()
        if self.encoding is not None:
            for level in X_train_series_names_in_:
                self.in_sample_residuals_[level] = None
                self.in_sample_residuals_by_bin_[level] = None
        self.in_sample_residuals_['_unknown_level'] = None
        self.in_sample_residuals_by_bin_['_unknown_level'] = None

    if store_last_window:
        self.last_window_ = last_window_

    set_skforecast_warnings(suppress_warnings, action='default')

_binning_in_sample_residuals

_binning_in_sample_residuals(
    level,
    y_true,
    y_pred,
    store_in_sample_residuals=False,
    random_state=123,
)

Bin residuals according to the predicted value each residual is associated with. First a skforecast.preprocessing.QuantileBinner object is fitted to the predicted values. Then, residuals are binned according to the predicted value each residual is associated with. Residuals are stored in the forecaster object as in_sample_residuals_ and in_sample_residuals_by_bin_.

y_true and y_pred assumed to be differentiated and/or transformed according to the attributes differentiation and transformer_series. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_. The total number of residuals stored is 10_000. New in version 0.15.0

Parameters:

Name	Type	Description	Default
y_true	numpy ndarray	True values of the time series.	required
y_pred	numpy ndarray	Predicted values of the time series.	required
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting (in_sample_residuals_ and in_sample_residuals_by_bin_ attributes). If False, only the intervals of the bins are stored.	False
random_state	int	Set a seed for the random generator so that the stored sample residuals are always deterministic.	123

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _binning_in_sample_residuals(
    self,
    level: str,
    y_true: np.ndarray,
    y_pred: np.ndarray,
    store_in_sample_residuals: bool = False,
    random_state: int = 123
) -> None:
    """
    Bin residuals according to the predicted value each residual is
    associated with. First a `skforecast.preprocessing.QuantileBinner` object
    is fitted to the predicted values. Then, residuals are binned according
    to the predicted value each residual is associated with. Residuals are
    stored in the forecaster object as `in_sample_residuals_` and
    `in_sample_residuals_by_bin_`.

    `y_true` and `y_pred` assumed to be differentiated and/or transformed
    according to the attributes `differentiation` and `transformer_series`.
    The number of residuals stored per bin is limited to 
    `10_000 // self.binner.n_bins_`. The total number of residuals stored is
    `10_000`.
    **New in version 0.15.0**

    Parameters
    ----------
    y_true : numpy ndarray
        True values of the time series.
    y_pred : numpy ndarray
        Predicted values of the time series.
    store_in_sample_residuals : bool, default False
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` and `in_sample_residuals_by_bin_`
        attributes).
        If `False`, only the intervals of the bins are stored.
    random_state : int, default 123
        Set a seed for the random generator so that the stored sample 
        residuals are always deterministic.

    Returns
    -------
    None

    """

    y_true = np.asarray(y_true)
    y_pred = np.asarray(y_pred)
    residuals = y_true - y_pred

    if self._probabilistic_mode == "binned":
        data = pd.DataFrame({'prediction': y_pred, 'residuals': residuals})
        self.binner[level] = QuantileBinner(**self.binner_kwargs)
        self.binner[level].fit(y_pred)
        self.binner_intervals_[level] = self.binner[level].intervals_

    if store_in_sample_residuals:
        rng = np.random.default_rng(seed=random_state)
        if self._probabilistic_mode == "binned":
            data['bin'] = self.binner[level].transform(y_pred).astype(int)
            self.in_sample_residuals_by_bin_[level] = (
                data.groupby('bin')['residuals'].apply(np.array).to_dict()
            )

            max_sample = 10_000 // self.binner[level].n_bins_
            for k, v in self.in_sample_residuals_by_bin_[level].items():
                if len(v) > max_sample:
                    sample = v[rng.integers(low=0, high=len(v), size=max_sample)]
                    self.in_sample_residuals_by_bin_[level][k] = sample

        if len(residuals) > 10_000:
            residuals = residuals[
                rng.integers(low=0, high=len(residuals), size=10_000)
            ]
        self.in_sample_residuals_[level] = residuals        

_create_predict_inputs

_create_predict_inputs(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    predict_probabilistic=False,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    check_inputs=True,
)

Create the inputs needed for the first iteration of the prediction process. As this is a recursive process, the last window is updated at each iteration of the prediction process.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	None
predict_probabilistic	bool	If True, the necessary checks for probabilistic predictions will be performed.	False
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True
check_inputs	bool	If True, the input is checked for possible warnings and errors with the check_predict_input function. This argument is created for internal use and is not recommended to be changed.	True

Returns:

Name	Type	Description
last_window	pandas DataFrame	Series values used to create the predictors needed in the first iteration of the prediction (t + 1).
exog_values_dict	(dict, None)	Exogenous variable/s included as predictor/s for each series in each step. The keys are the steps and the values are numpy arrays where each column is an exog and each row a series (level).
levels	list	Names of the series (levels) to be predicted.
prediction_index	pandas Index	Index of the predictions.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_predict_inputs(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    predict_probabilistic: bool = False,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    check_inputs: bool = True
) -> tuple[pd.DataFrame, dict[str, np.ndarray] | None, list[str], pd.Index]:
    """
    Create the inputs needed for the first iteration of the prediction 
    process. As this is a recursive process, the last window is updated at 
    each iteration of the prediction process.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    predict_probabilistic : bool, default False
        If `True`, the necessary checks for probabilistic predictions will be 
        performed.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
    check_inputs : bool, default True
        If `True`, the input is checked for possible warnings and errors 
        with the `check_predict_input` function. This argument is created 
        for internal use and is not recommended to be changed.

    Returns
    -------
    last_window : pandas DataFrame
        Series values used to create the predictors needed in the first 
        iteration of the prediction (t + 1).
    exog_values_dict : dict, None
        Exogenous variable/s included as predictor/s for each series in 
        each step. The keys are the steps and the values are numpy arrays
        where each column is an exog and each row a series (level).
    levels : list
        Names of the series (levels) to be predicted.
    prediction_index : pandas Index
        Index of the predictions.

    """

    input_levels_is_None = True if levels is None else False
    levels, input_levels_is_list = prepare_levels_multiseries(
        X_train_series_names_in_=self.X_train_series_names_in_, levels=levels
    )

    if self.is_fitted:
        if last_window is None:
            levels, last_window = preprocess_levels_self_last_window_multiseries(
                                      levels               = levels,
                                      input_levels_is_list = input_levels_is_list,
                                      last_window_         = self.last_window_
                                  )
        else:
            if input_levels_is_None and isinstance(last_window, pd.DataFrame):
                levels = last_window.columns.to_list()

    if check_inputs:
        check_predict_input(
            forecaster_name  = type(self).__name__,
            steps            = steps,
            is_fitted        = self.is_fitted,
            exog_in_         = self.exog_in_,
            index_type_      = self.index_type_,
            index_freq_      = self.index_freq_,
            window_size      = self.window_size,
            last_window      = last_window,
            exog             = exog,
            exog_type_in_    = self.exog_type_in_,
            exog_names_in_   = self.exog_names_in_,
            interval         = None,
            levels           = levels,
            series_names_in_ = self.series_names_in_,
            encoding         = self.encoding
        )

        if predict_probabilistic:
            check_residuals_input(
                forecaster_name              = type(self).__name__,
                use_in_sample_residuals      = use_in_sample_residuals,
                in_sample_residuals_         = self.in_sample_residuals_,
                out_sample_residuals_        = self.out_sample_residuals_,
                use_binned_residuals         = use_binned_residuals,
                in_sample_residuals_by_bin_  = self.in_sample_residuals_by_bin_,
                out_sample_residuals_by_bin_ = self.out_sample_residuals_by_bin_,
                levels                       = levels,
                encoding                     = self.encoding
            )

    last_window = last_window.iloc[
        -self.window_size :, last_window.columns.get_indexer(levels)
    ].copy()
    _, last_window_index = preprocess_last_window(
                               last_window   = last_window,
                               return_values = False
                           )
    prediction_index = expand_index(
                           index = last_window_index,
                           steps = steps
                       )

    if exog is not None:
        if isinstance(exog, dict):
            # Empty dataframe to be filled with the exog values of each level
            empty_exog = pd.DataFrame(
                             data  = {col: pd.Series(dtype=dtype)
                                      for col, dtype in self.exog_dtypes_in_.items()},
                             index = prediction_index
                         )
        else:
            if isinstance(exog, pd.Series):
                exog = exog.to_frame()

            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
            check_exog_dtypes(exog=exog)
            exog_values = exog.to_numpy()[:steps]
    else:
        exog_values = None

    exog_values_all_levels = []
    for level in levels:
        last_window_level = last_window[level].to_numpy()
        last_window_level = transform_numpy(
            array             = last_window_level,
            transformer       = self.transformer_series_.get(level, self.transformer_series_['_unknown_level']),
            fit               = False,
            inverse_transform = False
        )

        if self.differentiation is not None:
            if level not in self.differentiator_.keys():
                self.differentiator_[level] = copy(self.differentiator_['_unknown_level'])
            if self.differentiator_[level] is not None:
                last_window_level = (
                    self.differentiator_[level].fit_transform(last_window_level)
                )

        last_window[level] = last_window_level

        if isinstance(exog, dict):
            # Fill the empty dataframe with the exog values of each level
            # and transform them if necessary
            exog_values = exog.get(level, None)
            if exog_values is not None:
                if isinstance(exog_values, pd.Series):
                    exog_values = exog_values.to_frame()

                exog_values = empty_exog.fillna(exog_values)
                exog_values = transform_dataframe(
                                  df                = exog_values,
                                  transformer       = self.transformer_exog,
                                  fit               = False,
                                  inverse_transform = False
                              )

                check_exog_dtypes(
                    exog      = exog_values,
                    series_id = f"`exog` for series '{level}'"
                )
                exog_values = exog_values.to_numpy()
            else:
                exog_values = empty_exog.to_numpy(copy=True)

        exog_values_all_levels.append(exog_values)

    if exog is not None:
        # Exog is transformed into a dict where each key is a step and each value
        # is a numpy array where each column is an exog and each row a series
        exog_values_all_levels = np.concatenate(exog_values_all_levels)
        exog_values_dict = {}
        for i in range(steps):
            exog_values_dict[i + 1] = exog_values_all_levels[i::steps, :]
    else:
        exog_values_dict = None

    return last_window, exog_values_dict, levels, prediction_index

_recursive_predict

_recursive_predict(
    steps,
    levels,
    last_window,
    exog_values_dict=None,
    residuals=None,
    use_binned_residuals=True,
)

Predict n steps for one or multiple levels. It is an iterative process in which, each prediction, is used as a predictor for the next step.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	list	Time series to be predicted.	required
last_window	pandas DataFrame	Series values used to create the predictors needed in the first iteration of the prediction (t + 1).	required
exog_values_dict	dict	Exogenous variable/s included as predictor/s for each series in each step. The keys are the steps and the values are numpy arrays where each column is an exog and each row a series (level).	None
residuals	numpy ndarray	Residuals used to generate bootstrapping predictions in the form (steps, levels).	None
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly. New in version 0.15.0	True

Returns:

Name	Type	Description
predictions	numpy ndarray	Predicted values.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _recursive_predict(
    self,
    steps: int,
    levels: list,
    last_window: pd.DataFrame,
    exog_values_dict: dict[str, np.ndarray] | None = None,
    residuals: np.ndarray | None = None,
    use_binned_residuals: bool = True
) -> np.ndarray:
    """
    Predict n steps for one or multiple levels. It is an iterative process
    in which, each prediction, is used as a predictor for the next step.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : list
        Time series to be predicted.
    last_window : pandas DataFrame
        Series values used to create the predictors needed in the first 
        iteration of the prediction (t + 1).
    exog_values_dict : dict, default None
        Exogenous variable/s included as predictor/s for each series in 
        each step. The keys are the steps and the values are numpy arrays
        where each column is an exog and each row a series (level).
    residuals : numpy ndarray, default None
        Residuals used to generate bootstrapping predictions in the form
        (steps, levels).
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
        **New in version 0.15.0**

    Returns
    -------
    predictions : numpy ndarray
        Predicted values.

    """

    n_levels = len(levels)
    n_lags = len(self.lags) if self.lags is not None else 0
    n_window_features = (
        len(self.X_train_window_features_names_out_)
        if self.window_features is not None
        else 0
    )
    n_autoreg = n_lags + n_window_features
    n_exog = len(self.X_train_exog_names_out_) if exog_values_dict is not None else 0

    if self.encoding is not None:
        if self.encoding == "onehot":
            levels_encoded = np.zeros(
                (n_levels, len(self.X_train_series_names_in_)), dtype=float
            )
            for i, level in enumerate(levels):
                if level in self.X_train_series_names_in_:
                    levels_encoded[i, self.X_train_series_names_in_.index(level)] = 1.
        else:
            levels_encoded = np.array(
                [self.encoding_mapping_.get(level, None) for level in levels],
                dtype="float64"
            ).reshape(-1, 1)
        levels_encoded_shape = levels_encoded.shape[1]
    else:
        levels_encoded_shape = 0

    features_shape = n_autoreg + levels_encoded_shape + n_exog
    features = np.full(
        shape=(n_levels, features_shape), fill_value=np.nan, order='F', dtype=float
    )
    if self.encoding is not None:
        features[:, n_autoreg: n_autoreg + levels_encoded_shape] = levels_encoded

    predictions = np.full(
        shape=(steps, n_levels), fill_value=np.nan, order='C', dtype=float
    )
    last_window = np.concatenate((last_window.to_numpy(), predictions), axis=0)

    for i in range(steps):

        if self.lags is not None:
            features[:, :n_lags] = last_window[
                -self.lags - (steps - i), :
            ].transpose()
        if self.window_features is not None:
            features[:, n_lags:n_autoreg] = np.concatenate(
                [
                    wf.transform(last_window[i:-(steps - i), :]) 
                    for wf in self.window_features
                ],
                axis=1
            )
        if exog_values_dict is not None:
            features[:, -n_exog:] = exog_values_dict[i + 1]

        pred = self.regressor.predict(features)

        if residuals is not None:

            if use_binned_residuals:
                step_residual = np.full(
                    shape=n_levels, fill_value=np.nan, dtype=float
                )
                for j, level in enumerate(levels):
                    predicted_bin = (
                        self.binner
                        .get(level, self.binner['_unknown_level'])
                        .transform(pred[j])
                        .item()
                    )
                    step_residual[j] = residuals[predicted_bin][i, j]
            else:
                step_residual = residuals[i, :]

            pred += step_residual

        predictions[i, :] = pred 

        # Update `last_window` values. The first position is discarded and 
        # the new prediction is added at the end.
        last_window[-(steps - i), :] = pred

    return predictions

create_predict_X

create_predict_X(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    suppress_warnings=False,
)

Create the predictors needed to predict steps ahead. As it is a recursive process, the predictors are created at each iteration of the prediction process.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	None
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
X_predict_dict	dict	Dict in the form {level: X_predict} with the predictors for each step and series. The index is the same as the prediction index.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def create_predict_X(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    suppress_warnings: bool = False
) -> dict:
    """
    Create the predictors needed to predict `steps` ahead. As it is a recursive
    process, the predictors are created at each iteration of the prediction 
    process.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    X_predict_dict : dict
        Dict in the form `{level: X_predict}` with the predictors for each 
        step and series. The index is the same as the prediction index.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    (
        last_window,
        exog_values_dict,
        levels,
        prediction_index
    ) = self._create_predict_inputs(
            steps        = steps,
            levels       = levels,
            last_window  = last_window,
            exog         = exog
        )

    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", 
            message="X does not have valid feature names", 
            category=UserWarning
        )
        predictions = self._recursive_predict(
                          steps            = steps,
                          levels           = levels,
                          last_window      = last_window,
                          exog_values_dict = exog_values_dict
                      )

    X_predict_dict = {}
    if self.lags is not None:
        idx_lags = np.arange(-steps, 0)[:, None] - self.lags
    len_X_train_series_names_in_ = len(self.X_train_series_names_in_)
    exog_shape = len(self.X_train_exog_names_out_) if exog is not None else 0

    for i, level in enumerate(levels):

        X_predict_level = []
        full_predictors_level = np.concatenate(
            (last_window[level].to_numpy(), predictions[:, i])
        )

        if self.lags is not None:
            X_predict_level.append(
                full_predictors_level[idx_lags + len(full_predictors_level)]
            )

        if self.window_features is not None:
            X_window_features = np.full(
                shape      = (steps, len(self.X_train_window_features_names_out_)), 
                fill_value = np.nan, 
                order      = 'C',
                dtype      = float
            )
            for j in range(steps):
                X_window_features[j, :] = np.concatenate(
                    [
                        wf.transform(full_predictors_level[j:-(steps - j)]) 
                        for wf in self.window_features
                    ]
                )
            X_predict_level.append(X_window_features)

        if self.encoding is not None:
            if self.encoding == 'onehot':
                level_encoded = np.zeros(
                                    shape = (1, len_X_train_series_names_in_),
                                    dtype = float
                                )
                level_encoded[0][self.X_train_series_names_in_.index(level)] = 1.
            else:
                level_encoded = np.array(
                                    [self.encoding_mapping_.get(level, None)],
                                    dtype = 'float64'
                                )

            level_encoded = np.tile(level_encoded, (steps, 1))
            X_predict_level.append(level_encoded)

        if exog is not None:
            exog_cols = np.full(
                shape=(steps, exog_shape), fill_value=np.nan, order='C', dtype=float
            )
            for j in range(steps):
                exog_cols[j, :] = exog_values_dict[j + 1][i, :]
            X_predict_level.append(exog_cols)

        X_predict_dict[level] = pd.DataFrame(
                                    data    = np.concatenate(X_predict_level, axis=1),
                                    columns = self.X_train_features_names_out_,
                                    index   = prediction_index
                                )

    if self.transformer_series is not None or self.differentiation is not None:
        warnings.warn(
            "The output matrix is in the transformed scale due to the "
            "inclusion of transformations or differentiation in the Forecaster. "
            "As a result, any predictions generated using this matrix will also "
            "be in the transformed scale. Please refer to the documentation "
            "for more details: "
            "https://skforecast.org/latest/user_guides/training-and-prediction-matrices.html",
            DataTransformationWarning
        )

    set_skforecast_warnings(suppress_warnings, action='default')

    return X_predict_dict

predict

predict(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    suppress_warnings=False,
    check_inputs=True,
)

Predict n steps ahead. It is an recursive process in which, each prediction, is used as a predictor for the next step. Only levels whose last window ends at the same datetime index can be predicted together.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False
check_inputs	bool	If True, the input is checked for possible warnings and errors with the check_predict_input function. This argument is created for internal use and is not recommended to be changed.	True

Returns:

Name	Type	Description
predictions	pandas DataFrame	Long-format DataFrame with the predictions. The columns are level and pred.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    suppress_warnings: bool = False,
    check_inputs: bool = True
) -> pd.DataFrame:
    """
    Predict n steps ahead. It is an recursive process in which, each prediction,
    is used as a predictor for the next step. Only levels whose last window
    ends at the same datetime index can be predicted together.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.
    check_inputs : bool, default True
        If `True`, the input is checked for possible warnings and errors 
        with the `check_predict_input` function. This argument is created 
        for internal use and is not recommended to be changed.

    Returns
    -------
    predictions : pandas DataFrame
        Long-format DataFrame with the predictions. The columns are `level`
        and `pred`.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    (
        last_window,
        exog_values_dict,
        levels,
        prediction_index
    ) = self._create_predict_inputs(
        steps        = steps,
        levels       = levels,
        last_window  = last_window,
        exog         = exog,
        check_inputs = check_inputs
    )

    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", 
            message="X does not have valid feature names", 
            category=UserWarning
        )
        predictions = self._recursive_predict(
                          steps            = steps,
                          levels           = levels,
                          last_window      = last_window,
                          exog_values_dict = exog_values_dict
                      )

    for i, level in enumerate(levels):
        if self.differentiation is not None and self.differentiator_[level] is not None:
            predictions[:, i] = (
                self
                .differentiator_[level]
                .inverse_transform_next_window(predictions[:, i])
            )

        predictions[:, i] = transform_numpy(
            array             = predictions[:, i],
            transformer       = self.transformer_series_.get(level, self.transformer_series_['_unknown_level']),
            fit               = False,
            inverse_transform = True
        )

    n_steps, n_levels = predictions.shape
    predictions = pd.DataFrame(
        {"level": np.tile(levels, n_steps), "pred": predictions.ravel()},
        index = np.repeat(prediction_index, n_levels),
    )

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

predict_bootstrapping

predict_bootstrapping(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    n_boot=250,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    random_state=123,
    suppress_warnings=False,
)

Generate multiple forecasting predictions using a bootstrapping process. By sampling from a collection of past observed errors (the residuals), each iteration of bootstrapping generates a different set of predictions. Only levels whose last window ends at the same datetime index can be predicted together. See the References section for more information.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
n_boot	int	Number of bootstrapping iterations to perform when estimating prediction intervals.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly. New in version 0.15.0	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
boot_predictions	pandas DataFrame	Long-format DataFrame with the bootstrapping predictions. The columns are level, pred_boot_0, pred_boot_1, ..., pred_boot_n_boot.

References

.. [1] Forecasting: Principles and Practice (3^rd ed) Rob J Hyndman and George Athanasopoulos. https://otexts.com/fpp3/prediction-intervals.html

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_bootstrapping(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> pd.DataFrame:
    """
    Generate multiple forecasting predictions using a bootstrapping process. 
    By sampling from a collection of past observed errors (the residuals),
    each iteration of bootstrapping generates a different set of predictions. 
    Only levels whose last window ends at the same datetime index can be 
    predicted together. See the References section for more information. 

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating prediction
        intervals.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
        **New in version 0.15.0**
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    boot_predictions : pandas DataFrame
        Long-format DataFrame with the bootstrapping predictions. The columns
        are `level`, `pred_boot_0`, `pred_boot_1`, ..., `pred_boot_n_boot`.

    References
    ----------
    .. [1] Forecasting: Principles and Practice (3rd ed) Rob J Hyndman and George Athanasopoulos.
           https://otexts.com/fpp3/prediction-intervals.html

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    (
        last_window,
        exog_values_dict,
        levels,
        prediction_index
    ) = self._create_predict_inputs(
            steps                   = steps,
            levels                  = levels,
            last_window             = last_window,
            exog                    = exog,
            predict_probabilistic   = True,
            use_in_sample_residuals = use_in_sample_residuals,
            use_binned_residuals    = use_binned_residuals
        )

    if use_in_sample_residuals:
        residuals = self.in_sample_residuals_
        residuals_by_bin = self.in_sample_residuals_by_bin_
    else:
        residuals = self.out_sample_residuals_
        residuals_by_bin = self.out_sample_residuals_by_bin_

    n_levels = len(levels)
    rng = np.random.default_rng(seed=random_state)
    sampled_residuals_grid = np.full(
                                 shape      = (steps, n_boot, n_levels),
                                 fill_value = np.nan,
                                 order      = 'F',
                                 dtype      = float
                             )
    if use_binned_residuals:
        sampled_residuals = {
            k: sampled_residuals_grid.copy() 
            for k in range(self.binner_kwargs['n_bins'])
        }
        for bin in sampled_residuals.keys():
            for i, level in enumerate(levels):
                sampled_residuals[bin][:, :, i] = rng.choice(
                    a       = residuals_by_bin.get(level, residuals_by_bin['_unknown_level'])[bin],
                    size    = (steps, n_boot),
                    replace = True
                )
    else:
        for i, level in enumerate(levels):
            sampled_residuals_grid[:, :, i] = rng.choice(
                a       = residuals.get(level, residuals['_unknown_level']),
                size    = (steps, n_boot),
                replace = True
            )
        sampled_residuals = {'all': sampled_residuals_grid}

    boot_columns = []
    boot_predictions = np.full(
                           shape      = (steps, n_levels, n_boot),
                           fill_value = np.nan,
                           order      = 'F',
                           dtype      = float
                       )

    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", 
            message="X does not have valid feature names", 
            category=UserWarning
        )
        for i in range(n_boot):

            if use_binned_residuals:
                boot_sampled_residuals = {
                    k: v[:, i, :]
                    for k, v in sampled_residuals.items()
                }
            else:
                boot_sampled_residuals = sampled_residuals['all'][:, i, :]

            boot_columns.append(f"pred_boot_{i}")
            boot_predictions[:, :, i] = self._recursive_predict(
                steps                = steps,
                levels               = levels,
                last_window          = last_window,
                exog_values_dict     = exog_values_dict,
                residuals            = boot_sampled_residuals,
                use_binned_residuals = use_binned_residuals,
            )

    for i, level in enumerate(levels):

        if self.differentiation is not None and self.differentiator_[level] is not None:
            boot_predictions[:, i, :] = (
                self.differentiator_[level]
                .inverse_transform_next_window(boot_predictions[:, i, :])
            )

        transformer_level = self.transformer_series_.get(
                                level,
                                self.transformer_series_['_unknown_level']
                            )
        if transformer_level is not None:
            boot_predictions[:, i, :] = np.apply_along_axis(
                func1d            = transform_numpy,
                axis              = 0,
                arr               = boot_predictions[:, i, :],
                transformer       = transformer_level,
                fit               = False,
                inverse_transform = True
            )

    boot_predictions = pd.DataFrame(
                           data    = boot_predictions.reshape(-1, n_boot),
                           index   = np.repeat(prediction_index, n_levels),
                           columns = boot_columns
                       )
    boot_predictions.insert(0, 'level', np.tile(levels, steps))

    set_skforecast_warnings(suppress_warnings, action='default')

    return boot_predictions

_predict_interval_conformal

_predict_interval_conformal(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    nominal_coverage=0.95,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
)

Generate prediction intervals using the conformal prediction split method [1]_.

Parameters:

Name	Type	Description	Default
steps	int, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored inself.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	None
nominal_coverage	float	Nominal coverage, also known as expected coverage, of the prediction intervals. Must be between 0 and 1.	0.95
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True

Returns:

Name	Type	Description
predictions	pandas DataFrame	Values predicted by the forecaster and their estimated interval. pred: predictions. lower_bound: lower bound of the interval. upper_bound: upper bound of the interval.

References

.. [1] MAPIE - Model Agnostic Prediction Interval Estimator. https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _predict_interval_conformal(
    self,
    steps: int | str | pd.Timestamp,
    levels: str | list[str] | None = None,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    nominal_coverage: float = 0.95,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True
) -> pd.DataFrame:
    """
    Generate prediction intervals using the conformal prediction 
    split method [1]_.

    Parameters
    ----------
    steps : int, str, pandas Timestamp
        Number of steps to predict. 

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    nominal_coverage : float, default 0.95
        Nominal coverage, also known as expected coverage, of the prediction
        intervals. Must be between 0 and 1.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.

    Returns
    -------
    predictions : pandas DataFrame
        Values predicted by the forecaster and their estimated interval.

        - pred: predictions.
        - lower_bound: lower bound of the interval.
        - upper_bound: upper bound of the interval.

    References
    ----------
    .. [1] MAPIE - Model Agnostic Prediction Interval Estimator.
           https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

    """

    (
        last_window,
        exog_values_dict,
        levels,
        prediction_index
    ) = self._create_predict_inputs(
            steps                   = steps,
            levels                  = levels,
            last_window             = last_window,
            exog                    = exog,
            predict_probabilistic   = True,
            use_in_sample_residuals = use_in_sample_residuals,
            use_binned_residuals    = use_binned_residuals
        )

    if use_in_sample_residuals:
        residuals = self.in_sample_residuals_
        residuals_by_bin = self.in_sample_residuals_by_bin_
    else:
        residuals = self.out_sample_residuals_
        residuals_by_bin = self.out_sample_residuals_by_bin_

    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", 
            message="X does not have valid feature names", 
            category=UserWarning
        )
        predictions = self._recursive_predict(
                          steps            = steps,
                          levels           = levels,
                          last_window      = last_window,
                          exog_values_dict = exog_values_dict
                      )

    n_levels = len(levels)
    correction_factor = np.full(
        shape=(steps, n_levels), fill_value=np.nan, order='C', dtype=float
    )
    if use_binned_residuals:
        for i, level in enumerate(levels):
            residuals_level = residuals_by_bin.get(level, residuals_by_bin['_unknown_level'])
            correction_factor_by_bin = {
                k: np.quantile(np.abs(v), nominal_coverage)
                for k, v in residuals_level.items()
            }
            replace_func = np.vectorize(lambda x: correction_factor_by_bin[x])
            predictions_bin = (
                self.binner
                .get(level, self.binner['_unknown_level'])
                .transform(predictions[:, i])
            )
            correction_factor[:, i] = replace_func(predictions_bin)
    else:
        for i, level in enumerate(levels):
            correction_factor[:, i] = np.quantile(
                np.abs(residuals.get(level, residuals['_unknown_level'])), nominal_coverage
            )

    lower_bound = predictions - correction_factor
    upper_bound = predictions + correction_factor

    # NOTE: Create a 3D array with shape (n_levels, intervals, steps)
    predictions = np.array([predictions, lower_bound, upper_bound]).swapaxes(0, 2)

    for i, level in enumerate(levels):

        if self.differentiation is not None and self.differentiator_[level] is not None:
            predictions[i, :, :] = (
                self.differentiator_[level]
                .inverse_transform_next_window(predictions[i, :, :])
            )

        transformer_level = self.transformer_series_.get(
                                level,
                                self.transformer_series_['_unknown_level']
                            )
        if transformer_level is not None:
            predictions[i, :, :] = np.apply_along_axis(
                func1d            = transform_numpy,
                axis              = 0,
                arr               = predictions[i, :, :],
                transformer       = transformer_level,
                fit               = False,
                inverse_transform = True
            )

    predictions = pd.DataFrame(
                      data    = predictions.swapaxes(0, 1).reshape(-1, 3),
                      index   = np.repeat(prediction_index, n_levels),
                      columns = ["pred", "lower_bound", "upper_bound"]
                  )
    predictions.insert(0, 'level', np.tile(levels, steps))

    return predictions

predict_interval

predict_interval(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    method="conformal",
    interval=[5, 95],
    n_boot=250,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    random_state=123,
    suppress_warnings=False,
)

Predict n steps ahead and estimate prediction intervals using either bootstrapping or conformal prediction methods. Refer to the References section for additional details on these methods.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
method	str	Technique used to estimate prediction intervals. Available options: 'bootstrapping': Bootstrapping is used to generate prediction intervals [1]_. 'conformal': Employs the conformal prediction split method for interval estimation [2]_.	'conformal'
interval	(float, list, tuple)	Confidence level of the prediction interval. Interpretation depends on the method used: If float, represents the nominal (expected) coverage (between 0 and 1). For instance, interval=0.95 corresponds to [2.5, 97.5] percentiles. If list or tuple, defines the exact percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5]. When using method='conformal', the interval must be a float or a list/tuple defining a symmetric interval.	[5, 95]
n_boot	int	Number of bootstrapping iterations to perform when estimating prediction intervals.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly. New in version 0.15.0	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
predictions	pandas DataFrame	Long-format DataFrame with the predictions and the lower and upper bounds of the estimated interval. The columns are level, pred, lower_bound, upper_bound.

References

.. [1] Forecasting: Principles and Practice (3^rd ed) Rob J Hyndman and George Athanasopoulos. https://otexts.com/fpp3/prediction-intervals.html

.. [2] MAPIE - Model Agnostic Prediction Interval Estimator. https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_interval(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    method: str = 'conformal',
    interval: float | list[float] | tuple[float] = [5, 95],
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> pd.DataFrame:
    """
    Predict n steps ahead and estimate prediction intervals using either 
    bootstrapping or conformal prediction methods. Refer to the References 
    section for additional details on these methods.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    method : str, default 'conformal'
        Technique used to estimate prediction intervals. Available options:

        - 'bootstrapping': Bootstrapping is used to generate prediction 
        intervals [1]_.
        - 'conformal': Employs the conformal prediction split method for 
        interval estimation [2]_.
    interval : float, list, tuple, default [5, 95]
        Confidence level of the prediction interval. Interpretation depends 
        on the method used:

        - If `float`, represents the nominal (expected) coverage (between 0 
        and 1). For instance, `interval=0.95` corresponds to `[2.5, 97.5]` 
        percentiles.
        - If `list` or `tuple`, defines the exact percentiles to compute, which 
        must be between 0 and 100 inclusive. For example, interval 
        of 95% should be as `interval = [2.5, 97.5]`.
        - When using `method='conformal'`, the interval must be a float or 
        a list/tuple defining a symmetric interval.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating prediction
        intervals.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
        **New in version 0.15.0**
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    predictions : pandas DataFrame
        Long-format DataFrame with the predictions and the lower and upper
        bounds of the estimated interval. The columns are `level`, `pred`,
        `lower_bound`, `upper_bound`.

    References
    ----------
    .. [1] Forecasting: Principles and Practice (3rd ed) Rob J Hyndman and George Athanasopoulos.
           https://otexts.com/fpp3/prediction-intervals.html

    .. [2] MAPIE - Model Agnostic Prediction Interval Estimator.
           https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    if method == "bootstrapping":

        if isinstance(interval, (list, tuple)):
            check_interval(interval=interval, ensure_symmetric_intervals=False)
            interval = np.array(interval) / 100
        else:
            check_interval(alpha=interval, alpha_literal='interval')
            interval = np.array([0.5 - interval / 2, 0.5 + interval / 2])

        boot_predictions = self.predict_bootstrapping(
                               steps                   = steps,
                               levels                  = levels,
                               last_window             = last_window,
                               exog                    = exog,
                               n_boot                  = n_boot,
                               use_in_sample_residuals = use_in_sample_residuals,
                               use_binned_residuals    = use_binned_residuals,
                               random_state            = random_state,
                               suppress_warnings       = suppress_warnings
                           )

        predictions = self.predict(
                          steps             = steps,
                          levels            = levels,
                          last_window       = last_window,
                          exog              = exog,
                          suppress_warnings = suppress_warnings,
                          check_inputs      = False
                      )

        boot_predictions[['lower_bound', 'upper_bound']] = (
            boot_predictions.iloc[:, 1:].quantile(q=interval, axis=1).transpose()
        )
        predictions = pd.concat([
            predictions, boot_predictions[['lower_bound', 'upper_bound']]
        ], axis=1)

    elif method == 'conformal':

        if isinstance(interval, (list, tuple)):
            check_interval(interval=interval, ensure_symmetric_intervals=True)
            nominal_coverage = (interval[1] - interval[0]) / 100
        else:
            check_interval(alpha=interval, alpha_literal='interval')
            nominal_coverage = interval

        predictions = self._predict_interval_conformal(
                          steps                   = steps,
                          levels                  = levels,
                          last_window             = last_window,
                          exog                    = exog,
                          nominal_coverage        = nominal_coverage,
                          use_in_sample_residuals = use_in_sample_residuals,
                          use_binned_residuals    = use_binned_residuals
                      )
    else:
        raise ValueError(
            f"Invalid `method` '{method}'. Choose 'bootstrapping' or 'conformal'."
        )

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

predict_quantiles

predict_quantiles(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    quantiles=[0.05, 0.5, 0.95],
    n_boot=250,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    random_state=123,
    suppress_warnings=False,
)

Calculate the specified quantiles for each step. After generating multiple forecasting predictions through a bootstrapping process, each quantile is calculated for each step.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
quantiles	(list, tuple)	Sequence of quantiles to compute, which must be between 0 and 1 inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as quantiles = [0.05, 0.5, 0.95].	[0.05, 0.5, 0.95]
n_boot	int	Number of bootstrapping iterations to perform when estimating quantiles.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly. New in version 0.15.0	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
predictions	pandas DataFrame	Long-format DataFrame with the quantiles predicted by the forecaster. For example, if quantiles = [0.05, 0.5, 0.95], the columns are level, q_0.05, q_0.5, q_0.95.

References

.. [1] Forecasting: Principles and Practice (3^rd ed) Rob J Hyndman and George Athanasopoulos. https://otexts.com/fpp3/prediction-intervals.html

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_quantiles(
    self,
    steps: int,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    quantiles: list[float] | tuple[float] = [0.05, 0.5, 0.95],
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> pd.DataFrame:
    """
    Calculate the specified quantiles for each step. After generating 
    multiple forecasting predictions through a bootstrapping process, each 
    quantile is calculated for each step.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    quantiles : list, tuple, default [0.05, 0.5, 0.95]
        Sequence of quantiles to compute, which must be between 0 and 1 
        inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as 
        `quantiles = [0.05, 0.5, 0.95]`.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating quantiles.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
        **New in version 0.15.0**
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    predictions : pandas DataFrame
        Long-format DataFrame with the quantiles predicted by the forecaster.
        For example, if `quantiles = [0.05, 0.5, 0.95]`, the columns are
        `level`, `q_0.05`, `q_0.5`, `q_0.95`.

    References
    ----------
    .. [1] Forecasting: Principles and Practice (3rd ed) Rob J Hyndman and George Athanasopoulos.
           https://otexts.com/fpp3/prediction-intervals.html

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(quantiles=quantiles)

    predictions = self.predict_bootstrapping(
                      steps                   = steps,
                      levels                  = levels,
                      last_window             = last_window,
                      exog                    = exog,
                      n_boot                  = n_boot,
                      use_in_sample_residuals = use_in_sample_residuals,
                      use_binned_residuals    = use_binned_residuals,
                      random_state            = random_state,
                      suppress_warnings       = suppress_warnings
                  )

    quantiles_cols = [f'q_{q}' for q in quantiles]
    predictions[quantiles_cols] = (
        predictions.iloc[:, 1:].quantile(q=quantiles, axis=1).transpose()
    )
    predictions = predictions[['level'] + quantiles_cols]

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

predict_dist

predict_dist(
    steps,
    distribution,
    levels=None,
    last_window=None,
    exog=None,
    n_boot=250,
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    random_state=123,
    suppress_warnings=False,
)

Fit a given probability distribution for each step. After generating multiple forecasting predictions through a bootstrapping process, each step is fitted to the given distribution.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
distribution	object	A distribution object from scipy.stats with methods _pdf and fit. For example scipy.stats.norm.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	None
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
n_boot	int	Number of bootstrapping iterations to perform when estimating prediction intervals.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly. New in version 0.15.0	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Name	Type	Description
predictions	pandas DataFrame	Long-format DataFrame with the parameters of the fitted distribution for each step. The columns are level, param_0, param_1, ..., param_n, where param_i are the parameters of the distribution.

References

.. [1] Forecasting: Principles and Practice (3^rd ed) Rob J Hyndman and George Athanasopoulos. https://otexts.com/fpp3/prediction-intervals.html

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_dist(
    self,
    steps: int,
    distribution: object,
    levels: str | list[str] | None = None,
    last_window: pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> pd.DataFrame:
    """
    Fit a given probability distribution for each step. After generating 
    multiple forecasting predictions through a bootstrapping process, each 
    step is fitted to the given distribution.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    distribution : object
        A distribution object from scipy.stats with methods `_pdf` and `fit`. 
        For example scipy.stats.norm.
    levels : str, list, default None
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating prediction
        intervals.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
        **New in version 0.15.0**
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    predictions : pandas DataFrame
        Long-format DataFrame with the parameters of the fitted distribution
        for each step. The columns are `level`, `param_0`, `param_1`, ..., 
        `param_n`, where `param_i` are the parameters of the distribution.

    References
    ----------
    .. [1] Forecasting: Principles and Practice (3rd ed) Rob J Hyndman and George Athanasopoulos.
           https://otexts.com/fpp3/prediction-intervals.html

    """

    if not hasattr(distribution, "_pdf") or not callable(getattr(distribution, "fit", None)):
        raise TypeError(
            "`distribution` must be a valid probability distribution object "
            "from scipy.stats, with methods `_pdf` and `fit`."
        )

    set_skforecast_warnings(suppress_warnings, action='ignore')

    predictions = self.predict_bootstrapping(
                      steps                   = steps,
                      levels                  = levels,
                      last_window             = last_window,
                      exog                    = exog,
                      n_boot                  = n_boot,
                      use_in_sample_residuals = use_in_sample_residuals,
                      use_binned_residuals    = use_binned_residuals,
                      random_state            = random_state,
                      suppress_warnings       = suppress_warnings
                  )

    param_names = [
        p for p in inspect.signature(distribution._pdf).parameters 
        if not p == "x"
    ] + ["loc", "scale"]

    predictions[param_names] = (
        predictions.iloc[:, 1:].apply(
            lambda x: distribution.fit(x), axis=1, result_type='expand'
        )
    )
    predictions = predictions[['level'] + param_names]

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

set_params

set_params(params)

Set new values to the parameters of the scikit-learn model stored in the forecaster.

Parameters:

Name	Type	Description	Default
params	dict	Parameters values.	required

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_params(
    self, 
    params: dict[str, object]
) -> None:
    """
    Set new values to the parameters of the scikit-learn model stored in the
    forecaster.

    Parameters
    ----------
    params : dict
        Parameters values.

    Returns
    -------
    None

    """

    self.regressor = clone(self.regressor)
    self.regressor.set_params(**params)

set_fit_kwargs

set_fit_kwargs(fit_kwargs)

Set new values for the additional keyword arguments passed to the fit method of the regressor.

Parameters:

Name	Type	Description	Default
fit_kwargs	dict	Dict of the form {"argument": new_value}.	required

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_fit_kwargs(
    self, 
    fit_kwargs: dict[str, object]
) -> None:
    """
    Set new values for the additional keyword arguments passed to the `fit` 
    method of the regressor.

    Parameters
    ----------
    fit_kwargs : dict
        Dict of the form {"argument": new_value}.

    Returns
    -------
    None

    """

    self.fit_kwargs = check_select_fit_kwargs(self.regressor, fit_kwargs=fit_kwargs)

set_lags

set_lags(lags=None)

Set new value to the attribute lags. Attributes lags_names, max_lag and window_size are also updated.

Parameters:

Name	Type	Description	Default
lags	int, list, numpy ndarray, range	Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1. int: include lags from 1 to lags (included). list, 1d numpy ndarray or range: include only lags present in lags, all elements must be int. None: no lags are included as predictors.	None

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_lags(
    self, 
    lags: int | list[int] | np.ndarray[int] | range[int] | None = None
) -> None:
    """
    Set new value to the attribute `lags`. Attributes `lags_names`, 
    `max_lag` and `window_size` are also updated.

    Parameters
    ----------
    lags : int, list, numpy ndarray, range, default None
        Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1. 

        - `int`: include lags from 1 to `lags` (included).
        - `list`, `1d numpy ndarray` or `range`: include only lags present in 
        `lags`, all elements must be int.
        - `None`: no lags are included as predictors. 

    Returns
    -------
    None

    """

    if self.window_features is None and lags is None:
        raise ValueError(
            "At least one of the arguments `lags` or `window_features` "
            "must be different from None. This is required to create the "
            "predictors used in training the forecaster."
        )

    self.lags, self.lags_names, self.max_lag = initialize_lags(type(self).__name__, lags)
    self.window_size = max(
        [ws for ws in [self.max_lag, self.max_size_window_features] 
         if ws is not None]
    )

    if self.differentiation is not None:
        self.window_size += self.differentiation_max
        if isinstance(self.differentiator, dict):
            for series in self.differentiator.keys():
                if self.differentiator[series] is not None:
                    self.differentiator[series].set_params(window_size=self.window_size)
        else:
            self.differentiator.set_params(window_size=self.window_size)

set_window_features

set_window_features(window_features=None)

Set new value to the attribute window_features. Attributes max_size_window_features, window_features_names, window_features_class_names and window_size are also updated.

Parameters:

Name	Type	Description	Default
window_features	(object, list)	Instance or list of instances used to create window features. Window features are created from the original time series and are included as predictors.	None

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_window_features(
    self, 
    window_features: object | list[object] | None = None
) -> None:
    """
    Set new value to the attribute `window_features`. Attributes 
    `max_size_window_features`, `window_features_names`, 
    `window_features_class_names` and `window_size` are also updated.

    Parameters
    ----------
    window_features : object, list, default None
        Instance or list of instances used to create window features. Window features
        are created from the original time series and are included as predictors.

    Returns
    -------
    None

    """

    if window_features is None and self.lags is None:
        raise ValueError(
            "At least one of the arguments `lags` or `window_features` "
            "must be different from None. This is required to create the "
            "predictors used in training the forecaster."
        )

    self.window_features, self.window_features_names, self.max_size_window_features = (
        initialize_window_features(window_features)
    )
    self.window_features_class_names = None
    if window_features is not None:
        self.window_features_class_names = [
            type(wf).__name__ for wf in self.window_features
        ] 
    self.window_size = max(
        [ws for ws in [self.max_lag, self.max_size_window_features] 
         if ws is not None]
    )

    if self.differentiation is not None:
        self.window_size += self.differentiation_max
        if isinstance(self.differentiator, dict):
            for series in self.differentiator.keys():
                if self.differentiator[series] is not None:
                    self.differentiator[series].set_params(window_size=self.window_size)
        else:
            self.differentiator.set_params(window_size=self.window_size)

set_in_sample_residuals

set_in_sample_residuals(
    series,
    exog=None,
    random_state=123,
    suppress_warnings=False,
)

Set in-sample residuals in case they were not calculated during the training process.

In-sample residuals are calculated as the difference between the true values and the predictions made by the forecaster using the training data. The following internal attributes are updated:

• in_sample_residuals_: Dictionary containing a numpy ndarray with the residuals for each series in the form {series: residuals}.
• binner_intervals_: intervals used to bin the residuals are calculated using the quantiles of the predicted values.
• in_sample_residuals_by_bin_: residuals are binned according to the predicted value they are associated with and stored in a dictionary per series, where the keys are the intervals of the predicted values and the values are the residuals associated with that range.

A total of 10_000 residuals are stored in the attribute in_sample_residuals_. If the number of residuals is greater than 10_000, a random sample of 10_000 residuals is stored. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_.

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	None
random_state	int	Sets a seed to the random sampling for reproducible output.	123
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the sampling process. See skforecast.exceptions.warn_skforecast_categories for more information.	False

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_in_sample_residuals(
    self,
    series: pd.DataFrame | dict[str, pd.Series | pd.DataFrame],
    exog: pd.Series | pd.DataFrame | dict[str, pd.Series | pd.DataFrame] | None = None,
    random_state: int = 123,
    suppress_warnings: bool = False
) -> None:
    """
    Set in-sample residuals in case they were not calculated during the
    training process. 

    In-sample residuals are calculated as the difference between the true 
    values and the predictions made by the forecaster using the training 
    data. The following internal attributes are updated:

    + `in_sample_residuals_`: Dictionary containing a numpy ndarray with the
    residuals for each series in the form `{series: residuals}`.
    + `binner_intervals_`: intervals used to bin the residuals are calculated
    using the quantiles of the predicted values.
    + `in_sample_residuals_by_bin_`: residuals are binned according to the
    predicted value they are associated with and stored in a dictionary per
    series, where the keys are the intervals of the predicted values and the 
    values are the residuals associated with that range. 

    A total of 10_000 residuals are stored in the attribute `in_sample_residuals_`.
    If the number of residuals is greater than 10_000, a random sample of
    10_000 residuals is stored. The number of residuals stored per bin is
    limited to `10_000 // self.binner.n_bins_`.

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    exog : pandas Series, pandas DataFrame, dict, default None
        Exogenous variable/s included as predictor/s.
    random_state : int, default 123
        Sets a seed to the random sampling for reproducible output.
    suppress_warnings : bool, default False
        If `True`, skforecast warnings will be suppressed during the sampling 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    None

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    if not self.is_fitted:
        raise NotFittedError(
            "This forecaster is not fitted yet. Call `fit` with appropriate "
            "arguments before using `set_in_sample_residuals()`."
        )

    (
        X_train,
        y_train,
        series_indexes,
        _,
        X_train_series_names_in_,
        *_
    ) = self._create_train_X_y(
            series=series, exog=exog, store_last_window=False
        )

    # NOTE: Same series names as training is checked in _create_train_X_y.
    series_index_range = {k: v[[0, -1]] for k, v in series_indexes.items()}
    for level in self.training_range_.keys():
        if not series_index_range[level].equals(self.training_range_[level]):
            raise IndexError(
                f"The index range for series '{level}' does not match the range "
                f"used during training. Please ensure the index is aligned "
                f"with the training data.\n"
                f"    Expected : {self.training_range_[level]}\n"
                f"    Received : {series_index_range[level]}"
            )

    X_train_regressor = (
        X_train
        if self.encoding is not None
        else X_train.drop(columns="_level_skforecast")
    )
    X_train_features_names_out_ = X_train_regressor.columns.to_list()
    if not X_train_features_names_out_ == self.X_train_features_names_out_:
        raise ValueError(
            f"Feature mismatch detected after matrix creation. The features "
            f"generated from the provided data do not match those used during "
            f"the training process. To correctly set in-sample residuals, "
            f"ensure that the same data and preprocessing steps are applied.\n"
            f"    Expected output : {self.X_train_features_names_out_}\n"
            f"    Current output  : {X_train_features_names_out_}"
        )

    self.in_sample_residuals_ = {}
    self.in_sample_residuals_by_bin_ = {}
    y_pred = self.regressor.predict(X_train_regressor)
    if self.encoding is not None:
        for level in X_train_series_names_in_:
            if self.encoding == 'onehot':
                mask = X_train[level].to_numpy() == 1.
            else:
                encoded_value = self.encoding_mapping_[level]
                mask = X_train['_level_skforecast'].to_numpy() == encoded_value

            self._binning_in_sample_residuals(
                level                     = level,
                y_true                    = y_train[mask],
                y_pred                    = y_pred[mask],
                store_in_sample_residuals = True,
                random_state              = random_state
            )

    # NOTE: the _unknown_level is a random sample of 10_000 residuals of all levels.
    self._binning_in_sample_residuals(
        level                     = '_unknown_level',
        y_true                    = y_train,
        y_pred                    = y_pred,
        store_in_sample_residuals = True,
        random_state              = random_state
    )

    set_skforecast_warnings(suppress_warnings, action='default')

set_out_sample_residuals

set_out_sample_residuals(
    y_true, y_pred, append=False, random_state=123
)

Set new values to the attribute out_sample_residuals_. Out of sample residuals are meant to be calculated using observations that did not participate in the training process. y_true and y_pred are expected to be in the original scale of the time series. Residuals are calculated as y_true - y_pred, after applying the necessary transformations and differentiations if the forecaster includes them (self.transformer_series and self.differentiation).

A total of 10_000 residuals are stored in the attribute out_sample_residuals_. If the number of residuals is greater than 10_000, a random sample of 10_000 residuals is stored.

Parameters:

Name	Type	Description	Default
y_true	dict	Dictionary of numpy ndarrays or pandas Series with the true values of the time series for each series in the form {series: y_true}.	required
y_pred	dict	Dictionary of numpy ndarrays or pandas Series with the predicted values of the time series for each series in the form {series: y_pred}.	required
append	bool	If True, new residuals are added to the once already stored in the attribute out_sample_residuals_. If after appending the new residuals, the limit of 10_000 samples is exceeded, a random sample of 10_000 is kept.	False
random_state	int	Sets a seed to the random sampling for reproducible output.	123

Returns:

Type	Description
None

Notes

Out-of-sample residuals can only be stored for series seen during fit. To save residuals for unseen levels use the key '_unknown_level'.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_out_sample_residuals(
    self, 
    y_true: dict[str, np.ndarray | pd.Series],
    y_pred: dict[str, np.ndarray | pd.Series],
    append: bool = False,
    random_state: int = 123
) -> None:
    """
    Set new values to the attribute `out_sample_residuals_`. Out of sample
    residuals are meant to be calculated using observations that did not
    participate in the training process. `y_true` and `y_pred` are expected
    to be in the original scale of the time series. Residuals are calculated
    as `y_true` - `y_pred`, after applying the necessary transformations and
    differentiations if the forecaster includes them (`self.transformer_series`
    and `self.differentiation`).

    A total of 10_000 residuals are stored in the attribute `out_sample_residuals_`.
    If the number of residuals is greater than 10_000, a random sample of
    10_000 residuals is stored.

    Parameters
    ----------
    y_true : dict
        Dictionary of numpy ndarrays or pandas Series with the true values of
        the time series for each series in the form {series: y_true}.
    y_pred : dict
        Dictionary of numpy ndarrays or pandas Series with the predicted values
        of the time series for each series in the form {series: y_pred}.
    append : bool, default False
        If `True`, new residuals are added to the once already stored in the
        attribute `out_sample_residuals_`. If after appending the new residuals,
        the limit of 10_000 samples is exceeded, a random sample of 10_000 is
        kept.
    random_state : int, default 123
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    None

    Notes
    -----
    Out-of-sample residuals can only be stored for series seen during 
    fit. To save residuals for unseen levels use the key '_unknown_level'. 

    """

    if not self.is_fitted:
        raise NotFittedError(
            "This forecaster is not fitted yet. Call `fit` with appropriate "
            "arguments before using `set_out_sample_residuals()`."
        )

    if not isinstance(y_true, dict):
        raise TypeError(
            f"`y_true` must be a dictionary of numpy ndarrays or pandas Series. "
            f"Got {type(y_true)}."
        )

    if not isinstance(y_pred, dict):
        raise TypeError(
            f"`y_pred` must be a dictionary of numpy ndarrays or pandas Series. "
            f"Got {type(y_pred)}."
        )

    if not set(y_true.keys()) == set(y_pred.keys()):
        raise ValueError(
            f"`y_true` and `y_pred` must have the same keys. "
            f"Got {set(y_true.keys())} and {set(y_pred.keys())}."
        )

    for k in y_true.keys():
        if not isinstance(y_true[k], (np.ndarray, pd.Series)):
            raise TypeError(
                f"Values of `y_true` must be numpy ndarrays or pandas Series. "
                f"Got {type(y_true[k])} for series '{k}'."
            )
        if not isinstance(y_pred[k], (np.ndarray, pd.Series)):
            raise TypeError(
                f"Values of `y_pred` must be numpy ndarrays or pandas Series. "
                f"Got {type(y_pred[k])} for series '{k}'."
            )
        if len(y_true[k]) != len(y_pred[k]):
            raise ValueError(
                f"`y_true` and `y_pred` must have the same length. "
                f"Got {len(y_true[k])} and {len(y_pred[k])} for series '{k}'."
            )
        if isinstance(y_true[k], pd.Series) and isinstance(y_pred[k], pd.Series):
            if not y_true[k].index.equals(y_pred[k].index):
                raise ValueError(
                    f"When containing pandas Series, elements in `y_true` and "
                    f"`y_pred` must have the same index. Error with series '{k}'."
                )

    # NOTE: Out-of-sample residuals can only be stored for series seen during 
    # fit. To save residuals for unseen levels use the key '_unknown_level'. 
    series_names_in_ = self.series_names_in_ + ['_unknown_level']        
    if self.out_sample_residuals_ is None:
        if self.encoding is not None:
            self.out_sample_residuals_ = {level: None for level in series_names_in_}
            self.out_sample_residuals_by_bin_ = {level: {} for level in series_names_in_}
        else:
            self.out_sample_residuals_ = {'_unknown_level': None}
            self.out_sample_residuals_by_bin_ = {'_unknown_level': {}}

    series_to_update = set(y_pred.keys()).intersection(set(series_names_in_))
    if not series_to_update:
        raise ValueError(
            "Provided keys in `y_pred` and `y_true` do not match any series "
            "seen during `fit`. Residuals cannot be updated."
        )

    for level in series_to_update:
        residuals_level, residuals_by_bin_level = (
            self._binning_out_sample_residuals(
                level        = level,
                y_true       = y_true[level],
                y_pred       = y_pred[level],
                append       = append,
                random_state = random_state
            )
        )
        self.out_sample_residuals_[level] = residuals_level
        self.out_sample_residuals_by_bin_[level] = residuals_by_bin_level

    if self.encoding is None or '_unknown_level' not in series_to_update:
        if self.encoding is None and list(y_true.keys()) != ['_unknown_level']:
            warnings.warn(
                "As `encoding` is set to `None`, no distinction between levels "
                "is made. All residuals are stored in the '_unknown_level' key.",
                UnknownLevelWarning
            )

        # NOTE: when encoding is None, all levels are combined in '_unknown_level'.
        if list(self.out_sample_residuals_.keys()) != ['_unknown_level']:
            # To update completely _unknown_level later
            self.out_sample_residuals_.pop('_unknown_level', None)

        residuals_all_levels = np.concatenate(
            [
                value 
                for value in self.out_sample_residuals_.values()
                if value is not None
            ]
        )
        rng = np.random.default_rng(seed=random_state)
        if len(residuals_all_levels) > 10_000:
            residuals_all_levels = rng.choice(
                                       a       = residuals_all_levels,
                                       size    = 10_000,
                                       replace = False
                                   )

        all_bins_keys = set(
            bin_key 
            for dict_level_bins in self.out_sample_residuals_by_bin_.values()
            for bin_key in dict_level_bins.keys()
        )
        residuals_by_bin_all_levels = {
            bin_key: np.concatenate(
                [
                    dict_level_bins.get(bin_key, np.array([]))
                    for dict_level_bins in self.out_sample_residuals_by_bin_.values()
                ]
            )
            for bin_key in all_bins_keys
        }
        for key in residuals_by_bin_all_levels.keys():
            if len(residuals_by_bin_all_levels[key]) > 10_000:
                residuals_by_bin_all_levels[key] = rng.choice(
                    a       = residuals_by_bin_all_levels[key],
                    size    = 10_000,
                    replace = False
                )

        if self.encoding is None:
            self.out_sample_residuals_ = {'_unknown_level': residuals_all_levels}
            self.out_sample_residuals_by_bin_ = {'_unknown_level': residuals_by_bin_all_levels}
        else:
            self.out_sample_residuals_['_unknown_level'] = residuals_all_levels
            self.out_sample_residuals_by_bin_['_unknown_level'] = residuals_by_bin_all_levels

_binning_out_sample_residuals

_binning_out_sample_residuals(
    level, y_true, y_pred, append=False, random_state=123
)

Bin out sample residuals using the already fitted binner. y_true and y_pred are expected to be in the original scale of the time series. Residuals are calculated as y_true - y_pred, after applying the necessary transformations and differentiations if the forecaster includes them (self.transformer_series and self.differentiation).

Parameters:

Name	Type	Description	Default
level	str	Name of the level y_true and y_pred belong to.	required
y_true	numpy ndarray	True values of the time series.	required
y_pred	numpy ndarray	Predicted values of the time series.	required
append	bool	If True, new residuals are added to the once already stored in the attribute out_sample_residuals_. If after appending the new residuals, the limit of 10_000 samples is exceeded, a random sample of 10_000 is kept.	False
random_state	int	Sets a seed to the random sampling for reproducible output.	123

Returns:

Name	Type	Description
out_sample_residuals	numpy ndarray	Array with the residual for level.
out_sample_residuals_by_bin	dict	Dictionary with the residuals binned by the fitted binner for level.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _binning_out_sample_residuals(
    self,
    level: str,
    y_true: np.ndarray,
    y_pred: np.ndarray,
    append: bool = False,
    random_state: int = 123
) -> tuple[np.ndarray, dict[int, np.ndarray]]:
    """
    Bin out sample residuals using the already fitted binner.
    `y_true` and `y_pred` are expected to be in the original scale of the
    time series. Residuals are calculated as `y_true` - `y_pred`, after 
    applying the necessary transformations and differentiations if the
    forecaster includes them (`self.transformer_series` and `self.differentiation`).

    Parameters
    ----------
    level : str
        Name of the level y_true and y_pred belong to.
    y_true : numpy ndarray
        True values of the time series.
    y_pred : numpy ndarray
        Predicted values of the time series.
    append : bool, default False
        If `True`, new residuals are added to the once already stored in the
        attribute `out_sample_residuals_`. If after appending the new residuals,
        the limit of 10_000 samples is exceeded, a random sample of 10_000 is
        kept.
    random_state : int, default 123
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    out_sample_residuals : numpy ndarray
        Array with the residual for `level`.
    out_sample_residuals_by_bin : dict
        Dictionary with the residuals binned by the fitted binner for `level`.

    """

    # NOTE: if the level is not known or encoding is None, then transformer,
    # differentiator and binner used are the ones of "_unknown_level"
    transformer = self.transformer_series_.get(level, self.transformer_series_['_unknown_level'])
    differentiator = copy(
        self.differentiator_.get(level, self.differentiator_["_unknown_level"])
    )
    if differentiator is not None:
        differentiator.set_params(window_size=None)

    if isinstance(y_true, pd.Series):
        y_true = y_true.to_numpy()
    if isinstance(y_pred, pd.Series):
        y_pred = y_pred.to_numpy()

    if self.transformer_series:
        y_true = transform_numpy(
                     array             = y_true,
                     transformer       = transformer,
                     fit               = False,
                     inverse_transform = False
                 )
        y_pred = transform_numpy(
                     array             = y_pred,
                     transformer       = transformer,
                     fit               = False,
                     inverse_transform = False
                 )

    if differentiator is not None:
        y_true = differentiator.fit_transform(y_true)[differentiator.order:]
        y_pred = differentiator.fit_transform(y_pred)[differentiator.order:]

    data = pd.DataFrame(
        {'prediction': y_pred, 'residuals': y_true - y_pred}
    ).dropna()
    y_pred = data['prediction'].to_numpy()
    residuals = data['residuals'].to_numpy()

    binner = self.binner.get(level, self.binner['_unknown_level'])
    data['bin'] = binner.transform(y_pred).astype(int)
    residuals_by_bin = data.groupby('bin')['residuals'].apply(np.array).to_dict()

    out_sample_residuals = self.out_sample_residuals_.get(level, np.array([]))
    out_sample_residuals_by_bin = deepcopy(self.out_sample_residuals_by_bin_.get(level, {}))

    out_sample_residuals = (
        np.array([]) 
        if out_sample_residuals is None
        else out_sample_residuals
    )
    out_sample_residuals_by_bin = (
        {} 
        if out_sample_residuals_by_bin is None
        else out_sample_residuals_by_bin
    )
    if append:
        out_sample_residuals = np.concatenate([out_sample_residuals, residuals])
        for k, v in residuals_by_bin.items():
            if k in out_sample_residuals_by_bin:
                out_sample_residuals_by_bin[k] = np.concatenate(
                    (out_sample_residuals_by_bin[k], v)
                )
            else:
                out_sample_residuals_by_bin[k] = v
    else:
        out_sample_residuals = residuals
        out_sample_residuals_by_bin = residuals_by_bin

    max_samples = 10_000 // binner.n_bins_
    rng = np.random.default_rng(seed=random_state)
    for k, v in out_sample_residuals_by_bin.items():
        if len(v) > max_samples:
            sample = rng.choice(a=v, size=max_samples, replace=False)
            out_sample_residuals_by_bin[k] = sample

    for k in self.binner_intervals_.get(level, {}).keys():
        if k not in out_sample_residuals_by_bin:
            out_sample_residuals_by_bin[k] = np.array([])

    empty_bins = [
        k for k, v in out_sample_residuals_by_bin.items() 
        if v.size == 0
    ]
    if empty_bins:
        warnings.warn(
            f"The following bins of level '{level}' have no out of sample residuals: "
            f"{empty_bins}. No predicted values fall in the interval "
            f"{[self.binner_intervals_[level][bin] for bin in empty_bins]}. "
            f"Empty bins will be filled with a random sample of residuals.", 
            ResidualsUsageWarning
        )
        for k in empty_bins:
            out_sample_residuals_by_bin[k] = rng.choice(
                a       = out_sample_residuals,
                size    = min(max_samples, len(out_sample_residuals)),
                replace = False
            )

    if len(out_sample_residuals) > 10_000:
        out_sample_residuals = rng.choice(
            a       = out_sample_residuals, 
            size    = 10_000, 
            replace = False
        )

    return out_sample_residuals, out_sample_residuals_by_bin

get_feature_importances

get_feature_importances(sort_importance=True)

Return feature importances of the regressor stored in the forecaster. Only valid when regressor stores internally the feature importances in the attribute feature_importances_ or coef_.

Parameters:

Name	Type	Description	Default
sort_importance	bool	If True, sorts the feature importances in descending order.	True

Returns:

Name	Type	Description
feature_importances	pandas DataFrame	Feature importances associated with each predictor.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def get_feature_importances(
    self,
    sort_importance: bool = True
) -> pd.DataFrame:
    """
    Return feature importances of the regressor stored in the
    forecaster. Only valid when regressor stores internally the feature
    importances in the attribute `feature_importances_` or `coef_`.

    Parameters
    ----------
    sort_importance: bool, default True
        If `True`, sorts the feature importances in descending order.

    Returns
    -------
    feature_importances : pandas DataFrame
        Feature importances associated with each predictor.

    """

    if not self.is_fitted:
        raise NotFittedError(
            ("This forecaster is not fitted yet. Call `fit` with appropriate "
             "arguments before using `get_feature_importances()`.")
        )

    if isinstance(self.regressor, Pipeline):
        estimator = self.regressor[-1]
    else:
        estimator = self.regressor

    if hasattr(estimator, 'feature_importances_'):
        feature_importances = estimator.feature_importances_
    elif hasattr(estimator, 'coef_'):
        feature_importances = estimator.coef_
    else:
        warnings.warn(
            f"Impossible to access feature importances for regressor of type "
            f"{type(estimator)}. This method is only valid when the "
            f"regressor stores internally the feature importances in the "
            f"attribute `feature_importances_` or `coef_`."
        )
        feature_importances = None

    if feature_importances is not None:
        feature_importances = pd.DataFrame({
                                  'feature': self.X_train_features_names_out_,
                                  'importance': feature_importances
                              })
        if sort_importance:
            feature_importances = feature_importances.sort_values(
                                      by='importance', ascending=False
                                  )

    return feature_importances