ForecasterRecursive

skforecast.recursive._forecaster_recursive.ForecasterRecursive

ForecasterRecursive(
    estimator=None,
    lags=None,
    window_features=None,
    transformer_y=None,
    transformer_exog=None,
    weight_func=None,
    differentiation=None,
    fit_kwargs=None,
    binner_kwargs=None,
    forecaster_id=None,
    regressor=None,
)

Bases: ForecasterBase

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

Parameters:

Name	Type	Description	Default
estimator	estimator or pipeline compatible with the scikit-learn API	An instance of a estimator or pipeline compatible with the scikit-learn API.	None
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
transformer_y	object transformer (preprocessor)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. ColumnTransformers are not allowed since they do not have inverse_transform method. The transformation is applied to y before training the forecaster.	None
transformer_exog	object 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.	None
weight_func	Callable	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 estimator does not have the argument sample_weight in its fit method. The resulting sample_weight cannot have negative values.	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. Before returning a prediction, the differencing operation is reversed.	None
fit_kwargs	dict	Additional arguments to be passed to the fit method of the estimator.	None
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner used to discretize the residuals into k bins according to the predicted values associated with each residual. Available arguments are: n_bins, method, subsample, random_state and dtype. Argument method is passed internally to the function numpy.percentile. New in version 0.14.0	None
forecaster_id	(str, int)	Name used as an identifier of the forecaster.	None
regressor	estimator or pipeline compatible with the Keras API	Deprecated, alias for estimator.	None

Attributes:

Name	Type	Description
estimator	estimator or pipeline compatible with the scikit-learn API	An instance of a estimator 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.
transformer_y	object transformer (preprocessor)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. ColumnTransformers are not allowed since they do not have inverse_transform method. The transformation is applied to y before training the forecaster.
transformer_exog	object 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	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 estimator does not have the argument sample_weight in its fit method. The resulting sample_weight cannot have negative values.
source_code_weight_func	str	Source code of the custom function used to create weights.
differentiation	int	Order of differencing applied to the time series before training the forecaster.
differentiation_max	int	Maximum order of differentiation. For this Forecaster, it is equal to the value of the differentiation parameter.
differentiator	TimeSeriesDifferentiator	Skforecast object used to differentiate the time series.
last_window_	pandas DataFrame	This window represents the most recent data observed by the predictor during its training phase. It contains 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_	pandas Index	First and last values of index of the data used during training.
series_name_in_	str	Names of the series 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 or DataFrame) used in training.
exog_dtypes_in_	dict	Type of each exogenous variable/s used in training before the transformation applied by transformer_exog. If transformer_exog is not used, it is equal to exog_dtypes_out_.
exog_dtypes_out_	dict	Type of each exogenous variable/s used in training after the transformation applied by transformer_exog. If transformer_exog is not used, it is equal to exog_dtypes_in_.
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 estimator.
in_sample_residuals_	numpy ndarray	Residuals of the model when predicting training data. Only stored up to 10_000 values. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
in_sample_residuals_by_bin_	dict	In sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ in the form {bin: residuals}. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
out_sample_residuals_	numpy ndarray	Residuals of the model when predicting non-training data. Only stored up to 10_000 values. Use set_out_sample_residuals() method to set values. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
out_sample_residuals_by_bin_	dict	Out of sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ in the form {bin: residuals}. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
binner	QuantileBinner	QuantileBinner used to discretize residuals into k bins according to the predicted values associated with each residual.
binner_intervals_	dict	Intervals used to discretize residuals into k bins according to the predicted values associated with each residual.
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner.
creation_date	str	Date of creation.
is_fitted	bool	Tag to identify if the estimator 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.
__skforecast_tags__	dict	Tags associated with the forecaster.
_probabilistic_mode	(str, bool)	Private attribute used to indicate whether the forecaster should perform some calculations during backtesting.

Methods:

Name	Description
create_train_X_y	Create training matrices from univariate time series and exogenous
create_sample_weights	Create weights for each observation according to the forecaster's attribute
fit	Training Forecaster.
create_predict_X	Create the predictors needed to predict steps ahead. As it is a recursive
predict	Predict n steps ahead. It is an recursive process in which, each prediction,
predict_bootstrapping	Generate multiple forecasting predictions using a bootstrapping process.
predict_interval	Predict n steps ahead and estimate prediction intervals using either
predict_quantiles	Calculate the specified quantiles for each step. After generating
predict_dist	Fit a given probability distribution for each step. After generating
set_params	Set new values to the parameters of the scikit-learn model stored in the
set_fit_kwargs	Set new values for the additional keyword arguments passed to the fit
set_lags	Set new value to the attribute lags. Attributes lags_names,
set_window_features	Set new value to the attribute window_features. Attributes
set_in_sample_residuals	Set in-sample residuals in case they were not calculated during the
set_out_sample_residuals	Set new values to the attribute out_sample_residuals_. Out of sample
get_feature_importances	Return feature importances of the estimator stored in the forecaster.

Source code in skforecast/recursive/_forecaster_recursive.py

def __init__(
    self,
    estimator: object = None,
    lags: int | list[int] | np.ndarray[int] | range[int] | None = None,
    window_features: object | list[object] | None = None,
    transformer_y: object | None = None,
    transformer_exog: object | None = None,
    weight_func: Callable | None = None,
    differentiation: int | None = None,
    fit_kwargs: dict[str, object] | None = None,
    binner_kwargs: dict[str, object] | None = None,
    forecaster_id: str | int | None = None,
    regressor: object = None
) -> None:

    self.estimator                          = copy(initialize_estimator(estimator, regressor))
    self.transformer_y                      = transformer_y
    self.transformer_exog                   = transformer_exog
    self.weight_func                        = weight_func
    self.source_code_weight_func            = None
    self.differentiation                    = differentiation
    self.differentiation_max                = None
    self.differentiator                     = None
    self.last_window_                       = None
    self.index_type_                        = None
    self.index_freq_                        = None
    self.training_range_                    = None
    self.series_name_in_                    = None
    self.exog_in_                           = False
    self.exog_names_in_                     = None
    self.exog_type_in_                      = None
    self.exog_dtypes_in_                    = None
    self.exog_dtypes_out_                   = 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.in_sample_residuals_by_bin_        = None
    self.out_sample_residuals_by_bin_       = None
    self.creation_date                      = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.is_fitted                          = False
    self.fit_date                           = None
    self.skforecast_version                 = __version__
    self.python_version                     = sys.version.split(" ")[0]
    self.forecaster_id                      = forecaster_id
    self._probabilistic_mode                = "binned"

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

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

    self.weight_func, self.source_code_weight_func, _ = initialize_weights(
        forecaster_name = type(self).__name__, 
        estimator       = estimator, 
        weight_func     = weight_func, 
        series_weights  = None
    )

    if 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.differentiation = differentiation
        self.differentiation_max = differentiation
        self.window_size += differentiation
        self.differentiator = TimeSeriesDifferentiator(
            order=differentiation, window_size=self.window_size
        )

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

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

    self.__skforecast_tags__ = {
        "library": "skforecast",
        "forecaster_name": "ForecasterRecursive",
        "forecaster_task": "regression",
        "forecasting_scope": "single-series",  # single-series | global
        "forecasting_strategy": "recursive",   # recursive | direct | deep_learning
        "index_types_supported": ["pandas.RangeIndex", "pandas.DatetimeIndex"],
        "requires_index_frequency": True,

        "allowed_input_types_series": ["pandas.Series"],
        "supports_exog": True,
        "allowed_input_types_exog": ["pandas.Series", "pandas.DataFrame"],
        "handles_missing_values_series": False, 
        "handles_missing_values_exog": True, 

        "supports_lags": True,
        "supports_window_features": True,
        "supports_transformer_series": True,
        "supports_transformer_exog": True,
        "supports_weight_func": True,
        "supports_differentiation": True,

        "prediction_types": ["point", "interval", "bootstrapping", "quantiles", "distribution"],
        "supports_probabilistic": True,
        "probabilistic_methods": ["bootstrapping", "conformal"],
        "handles_binned_residuals": True
    }

estimator instance-attribute

estimator = copy(initialize_estimator(estimator, regressor))

transformer_y instance-attribute

transformer_y = transformer_y

transformer_exog instance-attribute

transformer_exog = transformer_exog

weight_func instance-attribute

weight_func = weight_func

source_code_weight_func instance-attribute

source_code_weight_func = None

differentiation instance-attribute

differentiation = differentiation

differentiation_max instance-attribute

differentiation_max = None

differentiator instance-attribute

differentiator = None

last_window_ instance-attribute

last_window_ = None

index_type_ instance-attribute

index_type_ = None

index_freq_ instance-attribute

index_freq_ = None

training_range_ instance-attribute

training_range_ = None

series_name_in_ instance-attribute

series_name_in_ = None

exog_in_ instance-attribute

exog_in_ = False

exog_names_in_ instance-attribute

exog_names_in_ = None

exog_type_in_ instance-attribute

exog_type_in_ = None

exog_dtypes_in_ instance-attribute

exog_dtypes_in_ = None

exog_dtypes_out_ instance-attribute

exog_dtypes_out_ = None

X_train_window_features_names_out_ instance-attribute

X_train_window_features_names_out_ = None

X_train_exog_names_out_ instance-attribute

X_train_exog_names_out_ = None

X_train_features_names_out_ instance-attribute

X_train_features_names_out_ = None

in_sample_residuals_ instance-attribute

in_sample_residuals_ = None

out_sample_residuals_ instance-attribute

out_sample_residuals_ = None

in_sample_residuals_by_bin_ instance-attribute

in_sample_residuals_by_bin_ = None

out_sample_residuals_by_bin_ instance-attribute

out_sample_residuals_by_bin_ = None

creation_date instance-attribute

creation_date = strftime('%Y-%m-%d %H:%M:%S')

is_fitted instance-attribute

is_fitted = False

fit_date instance-attribute

fit_date = None

skforecast_version instance-attribute

skforecast_version = __version__

python_version instance-attribute

python_version = split(' ')[0]

forecaster_id instance-attribute

forecaster_id = forecaster_id

_probabilistic_mode instance-attribute

_probabilistic_mode = 'binned'

window_size instance-attribute

window_size = max(
    [
        ws
        for ws in [max_lag, max_size_window_features]
        if ws is not None
    ]
)

window_features_class_names instance-attribute

window_features_class_names = None

fit_kwargs instance-attribute

fit_kwargs = check_select_fit_kwargs(
    estimator=estimator, fit_kwargs=fit_kwargs
)

binner_kwargs instance-attribute

binner_kwargs = binner_kwargs

binner instance-attribute

binner = QuantileBinner(**(binner_kwargs))

binner_intervals_ instance-attribute

binner_intervals_ = None

_repr_html_

_repr_html_()

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

Source code in skforecast/recursive/_forecaster_recursive.py

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

    (
        params,
        _,
        _,
        exog_names_in_,
        _,
    ) = self._preprocess_repr(
            estimator      = self.estimator,
            exog_names_in_ = self.exog_names_in_
        )

    style, unique_id = get_style_repr_html(self.is_fitted)

    content = f"""
    <div class="container-{unique_id}">
        <p style="font-size: 1.5em; font-weight: bold; margin-block-start: 0.83em; margin-block-end: 0.83em;">{type(self).__name__}</p>
        <details open>
            <summary>General Information</summary>
            <ul>
                <li><strong>Estimator:</strong> {type(self.estimator).__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 name:</strong> {self.series_name_in_}</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>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 y:</strong> {self.transformer_y}</li>
                <li><strong>Transformer for exog:</strong> {self.transformer_exog}</li>
            </ul>
        </details>
        <details>
            <summary>Training Information</summary>
            <ul>
                <li><strong>Training range:</strong> {self.training_range_.to_list() if self.is_fitted else 'Not fitted'}</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>Estimator Parameters</summary>
            <ul>
                {params}
            </ul>
        </details>
        <details>
            <summary>Fit Kwargs</summary>
            <ul>
                {self.fit_kwargs}
            </ul>
        </details>
        <p>
            <a href="https://skforecast.org/{__version__}/api/forecasterrecursive.html">&#128712 <strong>API Reference</strong></a>
            &nbsp;&nbsp;
            <a href="https://skforecast.org/{__version__}/user_guides/autoregressive-forecaster.html">&#128462 <strong>User Guide</strong></a>
        </p>
    </div>
    """

    return style + content

_create_lags

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

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

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

Parameters:

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

Returns:

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

Notes

Returned matrices are views into the original y so care must be taken when modifying them.

Source code in skforecast/recursive/_forecaster_recursive.py

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

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

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

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

    Notes
    -----
    Returned matrices are views into the original `y` so care must be taken
    when modifying them.

    """

    X_data = None
    if self.lags is not None:
        y_strided = np.lib.stride_tricks.sliding_window_view(y, self.window_size)[:-1]
        X_data = y_strided[:, self.window_size - self.lags]

        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)

Create window features from a time series.

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.py

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

    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

_create_train_X_y(y, exog=None)

Create training matrices from univariate time series and exogenous variables.

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and their indexes must be aligned.	None

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.
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.
X_train_features_names_out_	list	Names of the columns of the matrix created internally for training.
exog_dtypes_in_	dict	Type of each exogenous variable/s used in training before the transformation applied by transformer_exog. If transformer_exog is not used, it is equal to exog_dtypes_out_.
exog_dtypes_out_	dict	Type of each exogenous variable/s used in training after the transformation applied by transformer_exog. If transformer_exog is not used, it is equal to exog_dtypes_in_.

Source code in skforecast/recursive/_forecaster_recursive.py

def _create_train_X_y(
    self,
    y: pd.Series,
    exog: pd.Series | pd.DataFrame | None = None
) -> tuple[
    pd.DataFrame, 
    pd.Series, 
    list[str], 
    list[str], 
    list[str], 
    list[str], 
    dict[str, type],
    dict[str, type]
]:
    """
    Create training matrices from univariate time series and exogenous
    variables.

    Parameters
    ----------
    y : pandas Series
        Training time series.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and their indexes must be aligned.

    Returns
    -------
    X_train : pandas DataFrame
        Training values (predictors).
    y_train : pandas Series
        Values of the time series related to each row of `X_train`.
    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.
    X_train_features_names_out_ : list
        Names of the columns of the matrix created internally for training.
    exog_dtypes_in_ : dict
        Type of each exogenous variable/s used in training before the transformation
        applied by `transformer_exog`. If `transformer_exog` is not used, it
        is equal to `exog_dtypes_out_`.
    exog_dtypes_out_ : dict
        Type of each exogenous variable/s used in training after the transformation
        applied by `transformer_exog`. If `transformer_exog` is not used, it 
        is equal to `exog_dtypes_in_`.

    """

    check_y(y=y)
    y = input_to_frame(data=y, input_name='y')

    if len(y) <= self.window_size:
        raise ValueError(
            f"Length of `y` must be greater than the maximum window size "
            f"needed by the forecaster.\n"
            f"    Length `y`: {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}."
        )

    fit_transformer = False if self.is_fitted else True
    y = transform_dataframe(
            df                = y, 
            transformer       = self.transformer_y,
            fit               = fit_transformer,
            inverse_transform = False,
        )
    y_values, y_index = check_extract_values_and_index(data=y, data_label='`y`')
    train_index = y_index[self.window_size:]

    if self.differentiation is not None:
        if not self.is_fitted:
            y_values = self.differentiator.fit_transform(y_values)
        else:
            differentiator = copy(self.differentiator)
            y_values = differentiator.fit_transform(y_values)

    exog_names_in_ = None
    exog_dtypes_in_ = None
    exog_dtypes_out_ = None
    X_as_pandas = False
    if exog is not None:
        check_exog(exog=exog, allow_nan=True)
        exog = input_to_frame(data=exog, input_name='exog')
        _, exog_index = check_extract_values_and_index(
            data=exog, data_label='`exog`', ignore_freq=True, return_values=False
        )

        len_y = len(y_values)
        len_train_index = len(train_index)
        len_exog = len(exog)
        if not len_exog == len_y and not len_exog == len_train_index:
            raise ValueError(
                f"Length of `exog` must be equal to the length of `y` (if index is "
                f"fully aligned) or length of `y` - `window_size` (if `exog` "
                f"starts after the first `window_size` values).\n"
                f"    `exog`              : ({exog_index[0]} -- {exog_index[-1]})  (n={len_exog})\n"
                f"    `y`                 : ({y.index[0]} -- {y.index[-1]})  (n={len_y})\n"
                f"    `y` - `window_size` : ({train_index[0]} -- {train_index[-1]})  (n={len_train_index})"
            )

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

        exog = transform_dataframe(
                   df                = exog,
                   transformer       = self.transformer_exog,
                   fit               = fit_transformer,
                   inverse_transform = False
               )

        check_exog_dtypes(exog, call_check_exog=True)
        exog_dtypes_out_ = get_exog_dtypes(exog=exog)
        X_as_pandas = any(
            not pd.api.types.is_numeric_dtype(dtype) or pd.api.types.is_bool_dtype(dtype) 
            for dtype in set(exog.dtypes)
        )

        if len_exog == len_y:
            if not (exog_index == y_index).all():
                raise ValueError(
                    "When `exog` has the same length as `y`, the index of "
                    "`exog` must be aligned with the index of `y` "
                    "to ensure the correct alignment of values."
                )
            # The first `self.window_size` positions have to be removed from 
            # exog since they are not in X_train.
            exog = exog.iloc[self.window_size:, ]
        else:
            if not (exog_index == train_index).all():
                raise ValueError(
                    "When `exog` doesn't contain the first `window_size` observations, "
                    "the index of `exog` must be aligned with the index of `y` minus "
                    "the first `window_size` observations to ensure the correct "
                    "alignment of values."
                )

    X_train = []
    X_train_features_names_out_ = []

    X_train_lags, y_train = self._create_lags(
        y=y_values, X_as_pandas=X_as_pandas, train_index=train_index
    )
    if X_train_lags is not None:
        X_train.append(X_train_lags)
        X_train_features_names_out_.extend(self.lags_names)

    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=X_as_pandas, train_index=train_index
            )
        )
        X_train.extend(X_train_window_features)
        X_train_features_names_out_.extend(X_train_window_features_names_out_)

    X_train_exog_names_out_ = None
    if exog is not None:
        X_train_exog_names_out_ = exog.columns.to_list()  
        if not X_as_pandas:
            exog = exog.to_numpy()     
        X_train_features_names_out_.extend(X_train_exog_names_out_)
        X_train.append(exog)

    if len(X_train) == 1:
        X_train = X_train[0]
    else:
        if X_as_pandas:
            X_train = pd.concat(X_train, axis=1)
        else:
            X_train = np.concatenate(X_train, axis=1)

    if X_as_pandas:
        X_train.index = train_index
    else:
        X_train = pd.DataFrame(
                      data    = X_train,
                      index   = train_index,
                      columns = X_train_features_names_out_
                  )

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

    return (
        X_train,
        y_train,
        exog_names_in_,
        X_train_window_features_names_out_,
        X_train_exog_names_out_,
        X_train_features_names_out_,
        exog_dtypes_in_,
        exog_dtypes_out_
    )

create_train_X_y

create_train_X_y(y, exog=None)

Create training matrices from univariate time series and exogenous variables.

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and their indexes must be aligned.	None

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_data.

Source code in skforecast/recursive/_forecaster_recursive.py

def create_train_X_y(
    self,
    y: pd.Series,
    exog: pd.Series | pd.DataFrame | None = None,
) -> tuple[pd.DataFrame, pd.Series]:
    """
    Create training matrices from univariate time series and exogenous
    variables.

    Parameters
    ----------
    y : pandas Series
        Training time series.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and their indexes must be aligned.

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

    """

    output = self._create_train_X_y(y=y, exog=exog)

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

    return X_train, y_train

_train_test_split_one_step_ahead

_train_test_split_one_step_ahead(
    y, initial_train_size, exog=None
)

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

Parameters:

Name	Type	Description	Default
y	pandas Series	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	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and their indexes must be aligned.	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.

Source code in skforecast/recursive/_forecaster_recursive.py

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

    Parameters
    ----------
    y : pandas Series
        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, default None
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and their indexes must be aligned.

    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`.

    """

    is_fitted = self.is_fitted
    self.is_fitted = False
    X_train, y_train, *_ = self._create_train_X_y(
        y    = y.iloc[: initial_train_size],
        exog = exog.iloc[: initial_train_size] if exog is not None else None
    )

    test_init = initial_train_size - self.window_size
    self.is_fitted = True
    X_test, y_test, *_ = self._create_train_X_y(
        y    = y.iloc[test_init:],
        exog = exog.iloc[test_init:] if exog is not None else None
    )

    self.is_fitted = is_fitted

    return X_train, y_train, X_test, y_test

create_sample_weights

create_sample_weights(X_train)

Create weights for each observation according to the forecaster's attribute weight_func.

Parameters:

Name	Type	Description	Default
X_train	pandas DataFrame	Dataframe created with the create_train_X_y method, first return.	required

Returns:

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

Source code in skforecast/recursive/_forecaster_recursive.py

def create_sample_weights(
    self,
    X_train: pd.DataFrame,
) -> np.ndarray:
    """
    Create weights for each observation according to the forecaster's attribute
    `weight_func`.

    Parameters
    ----------
    X_train : pandas DataFrame
        Dataframe created with the `create_train_X_y` method, first return.

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

    """

    sample_weight = None

    if self.weight_func is not None:
        sample_weight = self.weight_func(X_train.index)

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

    return sample_weight

fit

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

Training Forecaster.

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

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and their indexes must be aligned so that y[i] is regressed on exog[i].	None
store_last_window	bool	Whether or not to store the last window (last_window_) of training data.	True
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting (in_sample_residuals_ and in_sample_residuals_by_bin_ attributes). If False, only the intervals of the bins are stored.	False
random_state	int	Set a seed for the random generator so that the stored sample residuals are always deterministic.	123

Returns:

Type	Description
None

Source code in skforecast/recursive/_forecaster_recursive.py

def fit(
    self,
    y: pd.Series,
    exog: pd.Series | pd.DataFrame | None = None,
    store_last_window: bool = True,
    store_in_sample_residuals: bool = False,
    random_state: int = 123
) -> None:
    """
    Training Forecaster.

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

    Parameters
    ----------
    y : pandas Series
        Training time series.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and their indexes must be aligned so
        that y[i] is regressed on exog[i].
    store_last_window : bool, default True
        Whether or not to store the last window (`last_window_`) of training data.
    store_in_sample_residuals : bool, default False
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` and `in_sample_residuals_by_bin_`
        attributes).
        If `False`, only the intervals of the bins are stored.
    random_state : int, default 123
        Set a seed for the random generator so that the stored sample 
        residuals are always deterministic.

    Returns
    -------
    None

    """

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

    (
        X_train,
        y_train,
        exog_names_in_,
        X_train_window_features_names_out_,
        X_train_exog_names_out_,
        X_train_features_names_out_,
        exog_dtypes_in_,
        exog_dtypes_out_
    ) = self._create_train_X_y(y=y, exog=exog)

    sample_weight = self.create_sample_weights(X_train=X_train)

    if sample_weight is not None:
        self.estimator.fit(
            X             = X_train,
            y             = y_train,
            sample_weight = sample_weight,
            **self.fit_kwargs
        )
    else:
        self.estimator.fit(X=X_train, y=y_train, **self.fit_kwargs)

    self.X_train_window_features_names_out_ = X_train_window_features_names_out_
    self.X_train_features_names_out_ = X_train_features_names_out_

    self.is_fitted = True
    self.series_name_in_ = y.name if y.name is not None else 'y'
    self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.training_range_ = y.index[[0, -1]]
    self.index_type_ = type(y.index)
    if isinstance(y.index, pd.DatetimeIndex):
        self.index_freq_ = y.index.freq
    else: 
        self.index_freq_ = y.index.step

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

    # NOTE: This is done to save time during fit in functions such as backtesting()
    if self._probabilistic_mode is not False:
        self._binning_in_sample_residuals(
            y_true                    = y_train.to_numpy(),
            y_pred                    = self.estimator.predict(X_train).ravel(),
            store_in_sample_residuals = store_in_sample_residuals,
            random_state              = random_state
        )

    if store_last_window:
        self.last_window_ = (
            y.iloc[-self.window_size:]
            .copy()
            .to_frame(name=y.name if y.name is not None else 'y')
        )

_binning_in_sample_residuals

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

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

y_true and y_pred assumed to be differentiated and or transformed according to the attributes differentiation and transformer_y. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_. The total number of residuals stored is 10_000. New in version 0.14.0

Parameters:

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

Returns:

Type	Description
None

Source code in skforecast/recursive/_forecaster_recursive.py

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

    `y_true` and `y_pred` assumed to be differentiated and or transformed
    according to the attributes `differentiation` and `transformer_y`.
    The number of residuals stored per bin is limited to 
    `10_000 // self.binner.n_bins_`. The total number of residuals stored is
    `10_000`.
    **New in version 0.14.0**

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

    Returns
    -------
    None

    """

    residuals = y_true - y_pred

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

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

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

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

        self.in_sample_residuals_ = residuals

_create_predict_inputs

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

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

Parameters:

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

Returns:

Name	Type	Description
last_window_values	numpy ndarray	Series values used to create the predictors needed in the first iteration of the prediction (t + 1).
exog_values	numpy ndarray, None	Exogenous variable/s included as predictor/s.
prediction_index	pandas Index	Index of the predictions.
steps	int	Number of future steps predicted.

Source code in skforecast/recursive/_forecaster_recursive.py

def _create_predict_inputs(
    self,
    steps: int | str | pd.Timestamp, 
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    predict_probabilistic: bool = False,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    check_inputs: bool = True
) -> tuple[np.ndarray, np.ndarray | None, pd.Index, int]:
    """
    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, str, pandas Timestamp
        Number of steps to predict. 

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

    Returns
    -------
    last_window_values : numpy ndarray
        Series values used to create the predictors needed in the first 
        iteration of the prediction (t + 1).
    exog_values : numpy ndarray, None
        Exogenous variable/s included as predictor/s.
    prediction_index : pandas Index
        Index of the predictions.
    steps: int
        Number of future steps predicted.

    """

    if last_window is None:
        last_window = self.last_window_

    if self.is_fitted:
        steps = date_to_index_position(
                    index        = last_window.index,
                    date_input   = steps,
                    method       = 'prediction',
                    date_literal = 'steps'
                )

    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_names_in_  = self.exog_names_in_,
            interval        = None
        )

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

    last_window_values = (
        last_window.iloc[-self.window_size:].to_numpy(copy=True).ravel()
    )
    last_window_values = transform_numpy(
                             array             = last_window_values,
                             transformer       = self.transformer_y,
                             fit               = False,
                             inverse_transform = False
                         )
    if self.differentiation is not None:
        last_window_values = self.differentiator.fit_transform(last_window_values)

    if exog is not None:

        exog = input_to_frame(data=exog, input_name='exog')
        if exog.columns.tolist() != self.exog_names_in_:
            exog = exog[self.exog_names_in_]

        exog = transform_dataframe(
                   df                = exog,
                   transformer       = self.transformer_exog,
                   fit               = False,
                   inverse_transform = False
               )

        # NOTE: Only check dtypes if they are not the same as seen in training
        if not exog.dtypes.to_dict() == self.exog_dtypes_out_:
            check_exog_dtypes(exog=exog)
        else:
            check_exog(exog=exog, allow_nan=False)

        exog_values = exog.to_numpy()[:steps]
    else:
        exog_values = None

    prediction_index = expand_index(
                           index = last_window.index,
                           steps = steps,
                       )

    return last_window_values, exog_values, prediction_index, steps

_recursive_predict

_recursive_predict(
    steps,
    last_window_values,
    exog_values=None,
    residuals=None,
    use_binned_residuals=True,
)

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

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
last_window_values	numpy ndarray	Series values used to create the predictors needed in the first iteration of the prediction (t + 1).	required
exog_values	numpy ndarray	Exogenous variable/s included as predictor/s.	None
residuals	numpy ndarray, dict	Residuals used to generate bootstrapping predictions.	None
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True

Returns:

Name	Type	Description
predictions	numpy ndarray	Predicted values.

Source code in skforecast/recursive/_forecaster_recursive.py

def _recursive_predict(
    self,
    steps: int,
    last_window_values: np.ndarray,
    exog_values: np.ndarray | None = None,
    residuals: np.ndarray | dict[str, np.ndarray] | None = None,
    use_binned_residuals: bool = True,
) -> np.ndarray:
    """
    Predict n steps ahead. It is an iterative process in which, each prediction,
    is used as a predictor for the next step.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    last_window_values : numpy ndarray
        Series values used to create the predictors needed in the first 
        iteration of the prediction (t + 1).
    exog_values : numpy ndarray, default None
        Exogenous variable/s included as predictor/s.
    residuals : numpy ndarray, dict, default None
        Residuals used to generate bootstrapping predictions.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.

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

    """

    original_device = set_cpu_gpu_device(estimator=self.estimator, device='cpu')

    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_exog = exog_values.shape[1] if exog_values is not None else 0

    X = np.full(
        shape=(n_lags + n_window_features + n_exog), fill_value=np.nan, dtype=float
    )
    predictions = np.full(shape=steps, fill_value=np.nan, dtype=float)
    last_window = np.concatenate((last_window_values, predictions))

    for i in range(steps):

        if self.lags is not None:
            X[:n_lags] = last_window[-self.lags - (steps - i)]
        if self.window_features is not None:
            X[n_lags : n_lags + n_window_features] = np.concatenate(
                [
                    wf.transform(last_window[i : -(steps - i)])
                    for wf in self.window_features
                ]
            )
        if exog_values is not None:
            X[n_lags + n_window_features:] = exog_values[i]

        pred = self.estimator.predict(X.reshape(1, -1)).ravel()

        if residuals is not None:
            if use_binned_residuals:
                predicted_bin = self.binner.transform(pred).item()
                step_residual = residuals[predicted_bin][i]
            else:
                step_residual = residuals[i]

            pred += step_residual

        pred = pred.item()
        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

    set_cpu_gpu_device(estimator=self.estimator, device=original_device)

    return predictions

create_predict_X

create_predict_X(
    steps, last_window=None, exog=None, check_inputs=True
)

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, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored 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
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
X_predict	pandas DataFrame	Pandas DataFrame with the predictors for each step. The index is the same as the prediction index.

Source code in skforecast/recursive/_forecaster_recursive.py

def create_predict_X(
    self,
    steps: int,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    check_inputs: bool = True
) -> pd.DataFrame:
    """
    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, str, pandas Timestamp
        Number of steps to predict. 

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    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
    -------
    X_predict : pandas DataFrame
        Pandas DataFrame with the predictors for each step. The index 
        is the same as the prediction index.

    """

    (
        last_window_values,
        exog_values,
        prediction_index,
        steps
    ) = self._create_predict_inputs(
            steps        = steps,
            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,
                          last_window_values = last_window_values,
                          exog_values        = exog_values
                      )

    X_predict = []
    full_predictors = np.concatenate((last_window_values, predictions))

    if self.lags is not None:
        idx = np.arange(-steps, 0)[:, None] - self.lags
        X_lags = full_predictors[idx + len(full_predictors)]
        X_predict.append(X_lags)

    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 i in range(steps):
            X_window_features[i, :] = np.concatenate(
                [wf.transform(full_predictors[i:-(steps - i)]) 
                 for wf in self.window_features]
            )
        X_predict.append(X_window_features)

    if exog is not None:
        X_predict.append(exog_values)

    X_predict = pd.DataFrame(
                    data    = np.concatenate(X_predict, axis=1),
                    columns = self.X_train_features_names_out_,
                    index   = prediction_index
                )

    if self.exog_in_:
        categorical_features = any(
            not pd.api.types.is_numeric_dtype(dtype) or pd.api.types.is_bool_dtype(dtype) 
            for dtype in set(self.exog_dtypes_out_.values())
        )
        if categorical_features:
            X_predict = X_predict.astype(self.exog_dtypes_out_)

    if self.transformer_y 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
        )

    return X_predict

predict

predict(
    steps, last_window=None, exog=None, 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.

Parameters:

Name	Type	Description	Default
steps	int, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored 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
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 Series	Predicted values.

Source code in skforecast/recursive/_forecaster_recursive.py

def predict(
    self,
    steps: int | str | pd.Timestamp,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    check_inputs: bool = True
) -> pd.Series:
    """
    Predict n steps ahead. It is an recursive process in which, each prediction,
    is used as a predictor for the next step.

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

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    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 Series
        Predicted values.

    """

    (
        last_window_values,
        exog_values,
        prediction_index,
        steps
    ) = self._create_predict_inputs(
            steps        = steps,
            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,
                          last_window_values = last_window_values,
                          exog_values        = exog_values
                      )

    if self.differentiation is not None:
        predictions = self.differentiator.inverse_transform_next_window(predictions)

    predictions = transform_numpy(
                      array             = predictions,
                      transformer       = self.transformer_y,
                      fit               = False,
                      inverse_transform = True
                  )

    predictions = pd.Series(
                      data  = predictions,
                      index = prediction_index,
                      name  = 'pred'
                  )

    return predictions

predict_bootstrapping

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

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. See the References section for more information.

Parameters:

Name	Type	Description	Default
steps	int, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored 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
n_boot	int	Number of bootstrapping iterations to perform when estimating prediction intervals.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123

Returns:

Name	Type	Description
boot_predictions	pandas DataFrame	Predictions generated by bootstrapping. Shape: (steps, n_boot)

References

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

Source code in skforecast/recursive/_forecaster_recursive.py

def predict_bootstrapping(
    self,
    steps: int | str | pd.Timestamp,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123
) -> pd.DataFrame:
    """
    Generate multiple forecasting predictions using a bootstrapping process.
    By sampling from a collection of past observed errors (the residuals),
    each iteration of bootstrapping generates a different set of predictions. 
    See the References section for more information. 

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

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating prediction
        intervals.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.

    Returns
    -------
    boot_predictions : pandas DataFrame
        Predictions generated by bootstrapping.
        Shape: (steps, n_boot)

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

    """

    (
        last_window_values,
        exog_values,
        prediction_index,
        steps
    ) = self._create_predict_inputs(
            steps                   = steps, 
            last_window             = last_window, 
            exog                    = exog,
            predict_probabilistic   = True, 
            use_in_sample_residuals = use_in_sample_residuals,
            use_binned_residuals    = use_binned_residuals
        )

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

    rng = np.random.default_rng(seed=random_state)
    if use_binned_residuals:
        sampled_residuals = {
            k: v[rng.integers(low=0, high=len(v), size=(steps, n_boot))]
            for k, v in residuals_by_bin.items()
        }
    else:
        sampled_residuals = residuals[
            rng.integers(low=0, high=len(residuals), size=(steps, n_boot))
        ]

    boot_columns = []
    boot_predictions = np.full(
                           shape      = (steps, n_boot),
                           fill_value = np.nan,
                           order      = 'F',
                           dtype      = float
                       )
    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", 
            message="X does not have valid feature names", 
            category=UserWarning
        )
        for i in range(n_boot):

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

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

    if self.differentiation is not None:
        boot_predictions = (
            self.differentiator.inverse_transform_next_window(boot_predictions)
        )

    if self.transformer_y:
        boot_predictions = np.apply_along_axis(
                               func1d            = transform_numpy,
                               axis              = 0,
                               arr               = boot_predictions,
                               transformer       = self.transformer_y,
                               fit               = False,
                               inverse_transform = True
                           )

    boot_predictions = pd.DataFrame(
                           data    = boot_predictions,
                           index   = prediction_index,
                           columns = boot_columns
                       )

    return boot_predictions

_predict_interval_conformal

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

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

Parameters:

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

Returns:

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

References

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

Source code in skforecast/recursive/_forecaster_recursive.py

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

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

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

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

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

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

    """

    (
        last_window_values,
        exog_values,
        prediction_index,
        steps
    ) = self._create_predict_inputs(
            steps                   = steps,
            last_window             = last_window,
            exog                    = exog,
            predict_probabilistic   = True,
            use_in_sample_residuals = use_in_sample_residuals,
            use_binned_residuals    = use_binned_residuals
        )

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

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

    if use_binned_residuals:
        correction_factor_by_bin = {
            k: np.quantile(np.abs(v), nominal_coverage)
            for k, v in residuals_by_bin.items()
        }
        replace_func = np.vectorize(lambda x: correction_factor_by_bin[x])
        predictions_bin = self.binner.transform(predictions)
        correction_factor = replace_func(predictions_bin)
    else:
        correction_factor = np.quantile(np.abs(residuals), nominal_coverage)

    lower_bound = predictions - correction_factor
    upper_bound = predictions + correction_factor
    predictions = np.column_stack([predictions, lower_bound, upper_bound])

    if self.differentiation is not None:
        predictions = (
            self.differentiator.inverse_transform_next_window(predictions)
        )

    if self.transformer_y:
        predictions = np.apply_along_axis(
                          func1d            = transform_numpy,
                          axis              = 0,
                          arr               = predictions,
                          transformer       = self.transformer_y,
                          fit               = False,
                          inverse_transform = True
                      )

    predictions = pd.DataFrame(
                      data    = predictions,
                      index   = prediction_index,
                      columns = ["pred", "lower_bound", "upper_bound"]
                  )

    return predictions

predict_interval

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

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

Parameters:

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

Returns:

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

References

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

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

Source code in skforecast/recursive/_forecaster_recursive.py

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

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

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    method : str, default 'bootstrapping'
        Technique used to estimate prediction intervals. Available options:

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

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

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

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

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

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

    """

    if method == "bootstrapping":

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

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

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

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

    elif method == 'conformal':

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

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

    return predictions

predict_quantiles

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

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, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored inself.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	None
quantiles	(list, tuple)	Sequence of quantiles to compute, which must be between 0 and 1 inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as quantiles = [0.05, 0.5, 0.95].	[0.05, 0.5, 0.95]
n_boot	int	Number of bootstrapping iterations to perform when estimating quantiles.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123

Returns:

Name	Type	Description
predictions	pandas DataFrame	Quantiles predicted by the forecaster.

References

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

Source code in skforecast/recursive/_forecaster_recursive.py

def predict_quantiles(
    self,
    steps: int | str | pd.Timestamp,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    quantiles: list[float] | tuple[float] = [0.05, 0.5, 0.95],
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
) -> 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, str, pandas Timestamp
        Number of steps to predict. 

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    quantiles : list, tuple, default [0.05, 0.5, 0.95]
        Sequence of quantiles to compute, which must be between 0 and 1 
        inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as 
        `quantiles = [0.05, 0.5, 0.95]`.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating quantiles.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.

    Returns
    -------
    predictions : pandas DataFrame
        Quantiles predicted by the forecaster.

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

    """

    check_interval(quantiles=quantiles)

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

    predictions = boot_predictions.quantile(q=quantiles, axis=1).transpose()
    predictions.columns = [f'q_{q}' for q in quantiles]

    return predictions

predict_dist

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

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, str, pandas Timestamp	Number of steps to predict. If steps is int, number of steps to predict. If str or pandas Datetime, the prediction will be up to that date.	required
distribution	object	A distribution object from scipy.stats with methods _pdf and fit. For example scipy.stats.norm.	required
last_window	pandas Series, pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored inself.last_window_ are used to calculate the initial predictors, and the predictions start right after training data.	None
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	None
n_boot	int	Number of bootstrapping iterations to perform when estimating prediction intervals.	250
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True
random_state	int	Seed for the random number generator to ensure reproducibility.	123

Returns:

Name	Type	Description
predictions	pandas DataFrame	Distribution parameters estimated for each step.

References

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

Source code in skforecast/recursive/_forecaster_recursive.py

def predict_dist(
    self,
    steps: int | str | pd.Timestamp,
    distribution: object,
    last_window: pd.Series | pd.DataFrame | None = None,
    exog: pd.Series | pd.DataFrame | None = None,
    n_boot: int = 250,
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: int = 123,
) -> 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, str, pandas Timestamp
        Number of steps to predict. 

        - If steps is int, number of steps to predict. 
        - If str or pandas Datetime, the prediction will be up to that date.
    distribution : object
        A distribution object from scipy.stats with methods `_pdf` and `fit`. 
        For example scipy.stats.norm.
    last_window : pandas Series, pandas DataFrame, default None
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).  
        If `last_window = None`, the values stored in` self.last_window_` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s.
    n_boot : int, default 250
        Number of bootstrapping iterations to perform when estimating prediction
        intervals.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
    random_state : int, default 123
        Seed for the random number generator to ensure reproducibility.

    Returns
    -------
    predictions : pandas DataFrame
        Distribution parameters estimated for each step.

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

    """

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

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

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

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

    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.py

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

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

    Returns
    -------
    None

    """

    self.estimator = clone(self.estimator)
    self.estimator.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 estimator.

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.py

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

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

    Returns
    -------
    None

    """

    self.fit_kwargs = check_select_fit_kwargs(self.estimator, 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.py

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

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

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

    Returns
    -------
    None

    """

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

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

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

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

    Returns
    -------
    None

    """

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

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

set_in_sample_residuals

set_in_sample_residuals(y, exog=None, random_state=123)

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

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

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

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

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and their indexes must be aligned so that y[i] is regressed on exog[i].	None
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.py

def set_in_sample_residuals(
    self,
    y: pd.Series,
    exog: pd.Series | pd.DataFrame | None = None,
    random_state: int = 123
) -> None:
    """
    Set in-sample residuals in case they were not calculated during the
    training process. 

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

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

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

    Parameters
    ----------
    y : pandas Series
        Training time series.
    exog : pandas Series, pandas DataFrame, default None
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and their indexes must be aligned so
        that y[i] is regressed on exog[i].
    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_in_sample_residuals()`."
        )

    check_y(y=y)
    y_index_range = check_extract_values_and_index(
        data=y, data_label='`y`', return_values=False
    )[1][[0, -1]]
    if not y_index_range.equals(self.training_range_):
        raise IndexError(
            f"The index range of `y` does not match the range "
            f"used during training. Please ensure the index is aligned "
            f"with the training data.\n"
            f"    Expected : {self.training_range_}\n"
            f"    Received : {y_index_range}"
        )

    (
        X_train,
        y_train,
        _,
        _,
        _,
        X_train_features_names_out_,
        *_
    ) = self._create_train_X_y(y=y, exog=exog)

    if not X_train_features_names_out_ == self.X_train_features_names_out_:
        raise ValueError(
            f"Feature mismatch detected after matrix creation. The features "
            f"generated from the provided data do not match those used during "
            f"the training process. To correctly set in-sample residuals, "
            f"ensure that the same data and preprocessing steps are applied.\n"
            f"    Expected output : {self.X_train_features_names_out_}\n"
            f"    Current output  : {X_train_features_names_out_}"
        )

    self._binning_in_sample_residuals(
        y_true                    = y_train.to_numpy(),
        y_pred                    = self.estimator.predict(X_train).ravel(),
        store_in_sample_residuals = True,
        random_state              = random_state
    )

set_out_sample_residuals

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

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

• out_sample_residuals_: residuals stored in a numpy ndarray.
• out_sample_residuals_by_bin_: residuals are binned according to the predicted value they are associated with and stored in a dictionary, where the keys are the intervals of the predicted values and the values are the residuals associated with that range. If a bin binning is empty, it is filled with a random sample of residuals from other bins. This is done to ensure that all bins have at least one residual and can be used in the prediction process.

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. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_.

Parameters:

Name	Type	Description	Default
y_true	numpy ndarray, pandas Series	True values of the time series from which the residuals have been calculated.	required
y_pred	numpy ndarray, pandas Series	Predicted values of the time series.	required
append	bool	If True, new residuals are added to the once already stored in the forecaster. If after appending the new residuals, the limit of 10_000 // self.binner.n_bins_ values per bin is reached, a random sample of residuals is stored.	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.py

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

    + `out_sample_residuals_`: residuals stored in a numpy ndarray.
    + `out_sample_residuals_by_bin_`: residuals are binned according to the
    predicted value they are associated with and stored in a dictionary, where
    the keys are the  intervals of the predicted values and the values are
    the residuals associated with that range. If a bin binning is empty, it
    is filled with a random sample of residuals from other bins. This is done
    to ensure that all bins have at least one residual and can be used in the
    prediction process.

    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. The number of residuals stored per bin is
    limited to `10_000 // self.binner.n_bins_`.

    Parameters
    ----------
    y_true : numpy ndarray, pandas Series
        True values of the time series from which the residuals have been
        calculated.
    y_pred : numpy ndarray, pandas Series
        Predicted values of the time series.
    append : bool, default False
        If `True`, new residuals are added to the once already stored in the
        forecaster. If after appending the new residuals, the limit of
        `10_000 // self.binner.n_bins_` values per bin is reached, a random
        sample of residuals is stored.
    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, (np.ndarray, pd.Series)):
        raise TypeError(
            f"`y_true` argument must be `numpy ndarray` or `pandas Series`. "
            f"Got {type(y_true)}."
        )

    if not isinstance(y_pred, (np.ndarray, pd.Series)):
        raise TypeError(
            f"`y_pred` argument must be `numpy ndarray` or `pandas Series`. "
            f"Got {type(y_pred)}."
        )

    if len(y_true) != len(y_pred):
        raise ValueError(
            f"`y_true` and `y_pred` must have the same length. "
            f"Got {len(y_true)} and {len(y_pred)}."
        )

    if isinstance(y_true, pd.Series) and isinstance(y_pred, pd.Series):
        if not y_true.index.equals(y_pred.index):
            raise ValueError(
                "`y_true` and `y_pred` must have the same index."
            )

    y_true = deepcopy(y_true)
    y_pred = deepcopy(y_pred)
    if not isinstance(y_pred, np.ndarray):
        y_pred = y_pred.to_numpy()
    if not isinstance(y_true, np.ndarray):
        y_true = y_true.to_numpy()

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

    if self.differentiation is not None:
        differentiator = copy(self.differentiator)
        differentiator.set_params(window_size=None)
        y_true = differentiator.fit_transform(y_true)[self.differentiation:]
        y_pred = differentiator.fit_transform(y_pred)[self.differentiation:]

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

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

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

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

    bin_keys = (
        []
        if self.binner_intervals_ is None
        else self.binner_intervals_.keys()
    )
    for k in bin_keys:
        if k not in out_sample_residuals_by_bin:
            out_sample_residuals_by_bin[k] = np.array([])

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

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

    self.out_sample_residuals_ = out_sample_residuals
    self.out_sample_residuals_by_bin_ = out_sample_residuals_by_bin

get_feature_importances

get_feature_importances(sort_importance=True)

Return feature importances of the estimator stored in the forecaster. Only valid when estimator stores internally the feature importances in the attribute feature_importances_ or coef_. Otherwise, returns None.

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.py

def get_feature_importances(
    self,
    sort_importance: bool = True
) -> pd.DataFrame:
    """
    Return feature importances of the estimator stored in the forecaster.
    Only valid when estimator stores internally the feature importances in the
    attribute `feature_importances_` or `coef_`. Otherwise, returns `None`.

    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.estimator, Pipeline):
        estimator = self.estimator[-1]
    else:
        estimator = self.estimator

    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 estimator of type "
            f"{type(estimator)}. This method is only valid when the "
            f"estimator 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