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,
    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	Order of differencing applied to the time series before training the forecaster. If None, no differencing is applied. 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. Differentiation is reversed in the output of predict() and predict_interval(). WARNING: This argument is newly introduced and requires special attention. It is still experimental and may undergo changes.	`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`
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	Order of differencing applied to the time series before training the forecaster.
differentiator	TimeSeriesDifferentiator	Skforecast object 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 1000 values in the form {level: residuals}. If transformer_series is not None, residuals are stored in the transformed scale.
out_sample_residuals_	dict	Residuals of the model when predicting non-training data. Only stored up to 1000 values in the form {level: residuals}. If transformer_series is not None, residuals are assumed to be in the transformed scale. Use set_out_sample_residuals() method to set values.
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.

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: Optional[Union[int, list, np.ndarray, range]] = None,
    window_features: Optional[Union[object, list]] = None,
    encoding: Optional[str] = 'ordinal',
    transformer_series: Optional[Union[object, dict]] = None,
    transformer_exog: Optional[object] = None,
    weight_func: Optional[Union[Callable, dict]] = None,
    series_weights: Optional[dict] = None,
    differentiation: Optional[int] = None,
    dropna_from_series: bool = False,
    fit_kwargs: Optional[dict] = None,
    forecaster_id: Optional[Union[str, int]] = 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.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.out_sample_residuals_              = 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.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
        ] 

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

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

    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."
        )

    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}."
            )

_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 = self._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 the combined style and content
    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: Optional[pd.Index] = None
) -> Tuple[Optional[Union[np.ndarray, pd.DataFrame]], 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, list]:
    """

    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: Optional[pd.DataFrame] = None
) -> Tuple[pd.DataFrame, list, 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.differentiation 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:
        n_diff = 0 if self.differentiation is None else self.differentiation
        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: Union[pd.DataFrame, dict],
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    store_last_window: Union[bool, list] = True,
) -> Tuple[pd.DataFrame, pd.Series, dict, list, list, list, list, list, dict, dict]:
    """
    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
                                   )

    if self.differentiation is None:
        self.differentiator_ = {serie: None for serie in series_names_in_}
    else:
        if not self.is_fitted:
            self.differentiator_ = {
                serie: copy(self.differentiator) for serie in series_names_in_
            }

    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, 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 create_train_X_y(
    self,
    series: Union[pd.DataFrame, dict],
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = 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: Union[pd.DataFrame, dict],
    initial_train_size: int,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = 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()])
        max_index = max([v.index[-1] for v in series.values()])
        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

create_sample_weights

create_sample_weights(series_names_in_, X_train)

Crate 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:
    """
    Crate 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
    weights_series = 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":
            weights_series = [
                np.repeat(self.series_weights_[serie], sum(X_train[serie]))
                for serie in series_names_in_
            ]
        else:
            weights_series = [
                np.repeat(
                    self.series_weights_[serie],
                    sum(X_train["_level_skforecast"] == self.encoding_mapping_[serie]),
                )
                for serie in series_names_in_
            ]

        weights_series = np.concatenate(weights_series)

    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: lambda x: np.ones_like(x, dtype=float) 
                                 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 weights_series is not None:
        weights = weights_series
        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=True,
    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_ attribute).	`True`
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: Union[pd.DataFrame, dict],
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    store_last_window: Union[bool, list] = True,
    store_in_sample_residuals: bool = True,
    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 `True`
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` attribute).
    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')

    # 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.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_

    in_sample_residuals_ = {}
    if store_in_sample_residuals:

        residuals = (y_train - self.regressor.predict(X_train_regressor)).to_numpy()

        rng = np.random.default_rng(seed=123)
        if self.encoding is not None:
            for col in X_train_series_names_in_:
                if self.encoding == 'onehot':
                    mask = X_train[col].to_numpy() == 1.
                else:
                    encoded_value = self.encoding_mapping_[col]
                    mask = X_train['_level_skforecast'].to_numpy() == encoded_value

                residuals_col = residuals[mask]
                if len(residuals_col) > 1000:
                    residuals_col = rng.choice(
                                        a       = residuals_col,
                                        size    = 1000,
                                        replace = False
                                    )
                in_sample_residuals_[col] = residuals_col

        if len(residuals) > 1000:
            in_sample_residuals_['_unknown_level'] = rng.choice(
                                                        a       = residuals,
                                                        size    = 1000,
                                                        replace = False
                                                    )
        else:
            in_sample_residuals_['_unknown_level'] = residuals
    else:
        if self.encoding is not None:
            for col in X_train_series_names_in_:
                in_sample_residuals_[col] = None
        in_sample_residuals_['_unknown_level'] = None

    self.in_sample_residuals_ = in_sample_residuals_

    if store_last_window:
        self.last_window_ = last_window_

    set_skforecast_warnings(suppress_warnings, action='default')

_create_predict_inputs

_create_predict_inputs(
    steps,
    levels=None,
    last_window=None,
    exog=None,
    predict_boot=False,
    use_in_sample_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 future steps predicted.	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_boot	bool	If True, residuals are returned to generate bootstrapping predictions.	`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 are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`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.
residuals	(dict, None)	Residuals used to generate bootstrapping predictions for each level in the form {level: residuals}. If predict_boot = False, residuals is None.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def _create_predict_inputs(
    self,
    steps: int,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    predict_boot: bool = False,
    use_in_sample_residuals: bool = True,
    check_inputs: bool = True
) -> Tuple[pd.DataFrame, Optional[dict], list, pd.Index, Optional[dict]]:
    """
    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 future steps predicted.
    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_boot : bool, default `False`
        If `True`, residuals are returned to generate bootstrapping predictions.
    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 are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    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.
    residuals : dict, None
        Residuals used to generate bootstrapping predictions for each level 
        in the form `{level: residuals}`. If `predict_boot = False`, 
        `residuals` is `None`.

    """

    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 and 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_
                              )

    if self.is_fitted and predict_boot:
        residuals = prepare_residuals_multiseries(
                        levels                  = levels,
                        use_in_sample_residuals = use_in_sample_residuals,
                        encoding                = self.encoding,
                        in_sample_residuals_    = self.in_sample_residuals_,
                        out_sample_residuals_   = self.out_sample_residuals_
                    )
    else:
        residuals = None

    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
        )

    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)
            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, residuals

_recursive_predict

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

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 future steps predicted.	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`

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: Optional[dict] = None,
    residuals: Optional[np.ndarray] = None
) -> 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 future steps predicted.
    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).

    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:
            pred += residuals[i, :]

        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 future steps predicted.	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: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = 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 future steps predicted.
    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 future steps predicted.	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	Predicted values, one column for each level.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict(
    self,
    steps: int,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = 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 future steps predicted.
    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
        Predicted values, one column for each level.

    """

    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:
            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
        )

    predictions = pd.DataFrame(
                      data    = predictions,
                      index   = prediction_index,
                      columns = 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,
    random_state=123,
    use_in_sample_residuals=True,
    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 Notes section for more information.

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	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 used to estimate predictions.	`250`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
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 are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
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	dict	Predictions generated by bootstrapping for each level.

Notes

More information about prediction intervals in forecasting: https://otexts.com/fpp3/prediction-intervals.html#prediction-intervals-from-bootstrapped-residuals Forecasting: Principles and Practice (3nd ed) Rob J Hyndman and George Athanasopoulos.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_bootstrapping(
    self,
    steps: int,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    n_boot: int = 250,
    random_state: int = 123,
    use_in_sample_residuals: bool = True,
    suppress_warnings: bool = False
) -> dict:
    """
    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 Notes section for more information. 

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    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 used to estimate predictions.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot predictions are always 
        deterministic.
    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 are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    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 : dict
        Predictions generated by bootstrapping for each level.
        {level: pandas DataFrame, shape (steps, n_boot)}

    Notes
    -----
    More information about prediction intervals in forecasting:
    https://otexts.com/fpp3/prediction-intervals.html#prediction-intervals-from-bootstrapped-residuals
    Forecasting: Principles and Practice (3nd ed) Rob J Hyndman and George Athanasopoulos.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    (
        last_window,
        exog_values_dict,
        levels,
        prediction_index,
        residuals
    ) = self._create_predict_inputs(
        steps                   = steps,
        levels                  = levels,
        last_window             = last_window,
        exog                    = exog,
        predict_boot            = True,
        use_in_sample_residuals = use_in_sample_residuals
    )

    n_levels = len(levels)
    rng = np.random.default_rng(seed=random_state)
    sample_residuals = np.full(
                           shape      = (steps, n_boot, n_levels),
                           fill_value = np.nan,
                           order      = 'F',
                           dtype      = float
                       )
    for i, level in enumerate(levels):
        sample_residuals[:, :, i] = rng.choice(
                                        a       = residuals[level],
                                        size    = (steps, n_boot),
                                        replace = True
                                    )

    boot_columns = []
    boot_predictions_full = 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):

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

    boot_predictions = {}
    for i, level in enumerate(levels):

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

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

        boot_predictions[level] = pd.DataFrame(
                                      data    = boot_predictions_full[:, i, :],
                                      index   = prediction_index,
                                      columns = boot_columns
                                  )

    set_skforecast_warnings(suppress_warnings, action='default')

    return boot_predictions

predict_interval

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

Iterative process in which, each prediction, is used as a predictor for the next step and bootstrapping is used to estimate prediction intervals. Both predictions and intervals are returned.

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	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`
interval	list	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5].	`[5, 95]`
n_boot	int	Number of bootstrapping iterations used to estimate prediction intervals.	`250`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
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 are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
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	Values predicted by the forecaster and their estimated interval. level: predictions. level_lower_bound: lower bound of the interval. level_upper_bound: upper bound of the interval.

Notes

More information about prediction intervals in forecasting: https://otexts.com/fpp2/prediction-intervals.html Forecasting: Principles and Practice (2^nd ed) Rob J Hyndman and George Athanasopoulos.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_interval(
    self,
    steps: int,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    interval: list = [5, 95],
    n_boot: int = 250,
    random_state: int = 123,
    use_in_sample_residuals: bool = True,
    suppress_warnings: bool = False
) -> pd.DataFrame:
    """
    Iterative process in which, each prediction, is used as a predictor
    for the next step and bootstrapping is used to estimate prediction
    intervals. Both predictions and intervals are returned.

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    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.
    interval : list, default `[5, 95]`
        Confidence of the prediction interval estimated. Sequence of 
        percentiles to compute, which must be between 0 and 100 inclusive. 
        For example, interval of 95% should be as `interval = [2.5, 97.5]`.
    n_boot : int, default `250`
        Number of bootstrapping iterations used to estimate prediction 
        intervals.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot predictions are always 
        deterministic.
    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 are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    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
        Values predicted by the forecaster and their estimated interval.

        - level: predictions.
        - level_lower_bound: lower bound of the interval.
        - level_upper_bound: upper bound of the interval.

    Notes
    -----
    More information about prediction intervals in forecasting:
    https://otexts.com/fpp2/prediction-intervals.html
    Forecasting: Principles and Practice (2nd ed) Rob J Hyndman and
    George Athanasopoulos.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(interval=interval)

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

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

    interval = np.array(interval) / 100
    predictions = []

    for level in preds.columns:
        preds_interval = boot_predictions[level].quantile(q=interval, axis=1).transpose()
        preds_interval.columns = [f'{level}_lower_bound', f'{level}_upper_bound']
        predictions.append(preds[level])
        predictions.append(preds_interval)

    predictions = pd.concat(predictions, axis=1)

    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,
    random_state=123,
    use_in_sample_residuals=True,
    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 future steps predicted.	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	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 used to estimate quantiles.	`250`
random_state	int	Sets a seed to the random generator, so that boot quantiles are always deterministic.	`123`
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create quantiles. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
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	Quantiles predicted by the forecaster.

Notes

More information about prediction intervals in forecasting: https://otexts.com/fpp2/prediction-intervals.html Forecasting: Principles and Practice (2^nd ed) Rob J Hyndman and George Athanasopoulos.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_quantiles(
    self,
    steps: int,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    quantiles: list = [0.05, 0.5, 0.95],
    n_boot: int = 250,
    random_state: int = 123,
    use_in_sample_residuals: bool = True,
    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 future steps predicted.
    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, 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 used to estimate quantiles.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot quantiles are always 
        deterministic.
    use_in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create quantiles. If `False`, out of sample 
        residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    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
        Quantiles predicted by the forecaster.

    Notes
    -----
    More information about prediction intervals in forecasting:
    https://otexts.com/fpp2/prediction-intervals.html
    Forecasting: Principles and Practice (2nd ed) Rob J Hyndman and
    George Athanasopoulos.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(quantiles=quantiles)

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

    predictions = []

    for level in boot_predictions.keys():
        preds_quantiles = (
            boot_predictions[level].quantile(q=quantiles, axis=1).transpose()
        )
        preds_quantiles.columns = [f'{level}_q_{q}' for q in quantiles]
        predictions.append(preds_quantiles)

    predictions = pd.concat(predictions, axis=1)

    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,
    random_state=123,
    use_in_sample_residuals=True,
    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 future steps predicted.	required
distribution	Object	A distribution object from scipy.stats. 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 used to estimate predictions.	`250`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
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 are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
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	Distribution parameters estimated for each step and level.

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def predict_dist(
    self,
    steps: int,
    distribution: object,
    levels: Optional[Union[str, list]] = None,
    last_window: Optional[pd.DataFrame] = None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]] = None,
    n_boot: int = 250,
    random_state: int = 123,
    use_in_sample_residuals: bool = True,
    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 future steps predicted.
    distribution : Object
        A distribution object from scipy.stats. 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 used to estimate predictions.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot predictions are always 
        deterministic.
    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 are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    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
        Distribution parameters estimated for each step and level.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

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

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

    for level in boot_samples.keys():
        param_values = np.apply_along_axis(
            lambda x: distribution.fit(x), axis=1, arr=boot_samples[level]
        )
        level_param_names = [f'{level}_{p}' for p in param_names]

        pred_level = pd.DataFrame(
                         data    = param_values,
                         columns = level_param_names,
                         index   = boot_samples[level].index
                     )

        predictions.append(pred_level)

    predictions = pd.concat(predictions, axis=1)

    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
) -> 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
) -> 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: Optional[Union[int, list, np.ndarray, range]] = 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
        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: Optional[Union[object, list]] = 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
        self.differentiator.set_params(window_size=self.window_size)

set_out_sample_residuals

set_out_sample_residuals(
    y_true, y_pred, append=True, 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

Source code in skforecast\recursive\_forecaster_recursive_multiseries.py

def set_out_sample_residuals(
    self, 
    y_true: dict,
    y_pred: dict,
    append: bool = True,
    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

    """

    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}'."
                )

    levels = self.series_names_in_ + ['_unknown_level']
    if self.out_sample_residuals_ is None and self.encoding is not None:
        self.out_sample_residuals_ = {level: None for level in levels}
    elif self.out_sample_residuals_ is None:
        self.out_sample_residuals_ = {'_unknown_level': None}

    series_to_update = set(y_pred.keys()).intersection(set(levels))
    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."
        )

    residuals = {}
    rng = np.random.default_rng(seed=random_state)
    y_true = y_true.copy()
    y_pred = y_pred.copy()
    if self.differentiation is not None:
        differentiator = copy(self.differentiator)
        differentiator.set_params(window_size=None)

    for k in series_to_update:
        if isinstance(y_true[k], pd.Series):
            y_true[k] = y_true[k].to_numpy()
        if isinstance(y_pred[k], pd.Series):
            y_pred[k] = y_pred[k].to_numpy()
        if self.transformer_series:
            y_true[k] = transform_numpy(
                            array             = y_true[k],
                            transformer       = self.transformer_series_[k],
                            fit               = False,
                            inverse_transform = False
                        )
            y_pred[k] = transform_numpy(
                            array             = y_pred[k],
                            transformer       = self.transformer_series_[k],
                            fit               = False,
                            inverse_transform = False
                        )
        if self.differentiation is not None:
            y_true[k] = differentiator.fit_transform(y_true[k])[self.differentiation:]
            y_pred[k] = differentiator.fit_transform(y_pred[k])[self.differentiation:]

        residuals[k] = y_true[k] - y_pred[k]

    if '_unknown_level' not in residuals:
        residuals['_unknown_level'] = np.concatenate(list(residuals.values()))

    if self.encoding is None:
        if list(residuals.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
            )
        residuals = {'_unknown_level': residuals['_unknown_level']}

    for key, value in residuals.items():
        if append and self.out_sample_residuals_[key] is not None:
            value = np.concatenate((
                        self.out_sample_residuals_[key],
                        value
                    ))
        if len(value) > 10000:
            value = rng.choice(value, size=10000, replace=False)
        self.out_sample_residuals_[key] = value

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