ForecasterAutoreg

ForecasterAutoreg(regressor, lags, transformer_y=None, transformer_exog=None, weight_func=None, fit_kwargs=None, forecaster_id=None)

Bases: ForecasterBase

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

Parameters:

Name	Type	Description	Default
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API	required
lags	int, list, numpy ndarray, range	Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1. int: include lags from 1 to lags (included). list, 1d numpy ndarray or range: include only lags present in lags, all elements must be int.	required
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 regressor does not have the argument sample_weight in its fit method. The resulting sample_weight cannot have negative values.	`None`
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor. New in version 0.8.0	`None`
forecaster_id	str, int	Name used as an identifier of the forecaster. New in version 0.7.0	`None`

Attributes:

Name	Type	Description
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API.
lags	numpy ndarray	Lags used as predictors.
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 regressor 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.
max_lag	int	Maximum value of lag included in lags.
window_size	int	Size of the window needed to create the predictors. It is equal to max_lag.
last_window	pandas Series	Last window the forecaster has seen during training. It stores the values needed to predict the next step immediately after the training data.
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.
included_exog	bool	If the forecaster has been trained using exogenous variable/s.
exog_type	type	Type of exogenous data (pandas Series or DataFrame) used in training.
exog_dtypes	dict	Type of each exogenous variable/s used in training. If transformer_exog is used, the dtypes are calculated after the transformation.
exog_col_names	list	Names of columns of exog if exog used in training was a pandas DataFrame.
X_train_col_names	list	Names of columns of the matrix created internally for training.
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor. New in version 0.8.0
in_sample_residuals	numpy ndarray	Residuals of the model when predicting training data. Only stored up to 1000 values. If transformer_y is not None, residuals are stored in the transformed scale.
out_sample_residuals	numpy ndarray	Residuals of the model when predicting non training data. Only stored up to 1000 values. If transformer_y is not None, residuals are assumed to be in the transformed scale. Use set_out_sample_residuals method to set values.
fitted	bool	Tag to identify if the regressor has been fitted (trained).
creation_date	str	Date of creation.
fit_date	str	Date of last fit.
skforcast_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.

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def __init__(
    self,
    regressor: object,
    lags: Union[int, np.ndarray, list],
    transformer_y: Optional[object]=None,
    transformer_exog: Optional[object]=None,
    weight_func: Optional[Callable]=None,
    fit_kwargs: Optional[dict]=None,
    forecaster_id: Optional[Union[str, int]]=None
) -> None:

    self.regressor               = regressor
    self.transformer_y           = transformer_y
    self.transformer_exog        = transformer_exog
    self.weight_func             = weight_func
    self.source_code_weight_func = None
    self.last_window             = None
    self.index_type              = None
    self.index_freq              = None
    self.training_range          = None
    self.included_exog           = False
    self.exog_type               = None
    self.exog_dtypes             = None
    self.exog_col_names          = None
    self.X_train_col_names       = None
    self.in_sample_residuals     = None
    self.out_sample_residuals    = None
    self.fitted                  = False
    self.creation_date           = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.fit_date                = None
    self.skforcast_version       = skforecast.__version__
    self.python_version          = sys.version.split(" ")[0]
    self.forecaster_id           = forecaster_id

    self.lags = initialize_lags(type(self).__name__, lags)
    self.max_lag = max(self.lags)
    self.window_size = self.max_lag

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

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

_create_lags(y)

Transforms a 1d array into a 2d array (X) and a 1d array (y). Each row in X is associated with a value of y and it represents the lags that precede it.

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

Parameters:

Name	Type	Description	Default
y	numpy ndarray	1d numpy ndarray Training time series.	required

Returns:

Name	Type	Description
X_data	numpy ndarray	2d numpy ndarray with the lagged values (predictors). Shape: (samples - max(self.lags), len(self.lags))
y_data	numpy ndarray	1d numpy ndarray with the values of the time series related to each row of X_data. Shape: (samples - max(self.lags), )

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def _create_lags(
    self, 
    y: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
    """
    Transforms a 1d array into a 2d array (X) and a 1d array (y). Each row
    in X is associated with a value of y and it represents the lags that
    precede it.

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

    Parameters
    ----------
    y : numpy ndarray
        1d numpy ndarray Training time series.

    Returns
    -------
    X_data : numpy ndarray
        2d numpy ndarray with the lagged values (predictors). 
        Shape: (samples - max(self.lags), len(self.lags))
    y_data : numpy ndarray
        1d numpy ndarray with the values of the time series related to each 
        row of `X_data`. 
        Shape: (samples - max(self.lags), )

    """

    n_splits = len(y) - self.max_lag
    if n_splits <= 0:
        raise ValueError(
            (f"The maximum lag ({self.max_lag}) must be less than the length "
             f"of the series ({len(y)}).")
        )

    X_data = np.full(shape=(n_splits, len(self.lags)), fill_value=np.nan, dtype=float)

    for i, lag in enumerate(self.lags):
        X_data[:, i] = y[self.max_lag - lag: -lag]

    y_data = y[self.max_lag:]

    return X_data, y_data

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). Shape: (len(y) - self.max_lag, len(self.lags))
y_train	pandas Series	Values (target) of the time series related to each row of X_train. Shape: (len(y) - self.max_lag, )

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def create_train_X_y(
    self,
    y: pd.Series,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=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).
        Shape: (len(y) - self.max_lag, len(self.lags))
    y_train : pandas Series
        Values (target) of the time series related to each row of `X_train`.
        Shape: (len(y) - self.max_lag, )

    """

    check_y(y=y)
    y = transform_series(
            series            = y,
            transformer       = self.transformer_y,
            fit               = True,
            inverse_transform = False
        )
    y_values, y_index = preprocess_y(y=y)

    if exog is not None:
        if len(exog) != len(y):
            raise ValueError(
                (f'`exog` must have same number of samples as `y`. '
                 f'length `exog`: ({len(exog)}), length `y`: ({len(y)})')
            )
        check_exog(exog=exog, allow_nan=True)
        if isinstance(exog, pd.Series):
            exog = transform_series(
                       series            = exog,
                       transformer       = self.transformer_exog,
                       fit               = True,
                       inverse_transform = False
                   )
        else:
            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = True,
                       inverse_transform = False
                   )

        check_exog(exog=exog, allow_nan=False)
        check_exog_dtypes(exog)
        self.exog_dtypes = get_exog_dtypes(exog=exog)

        _, exog_index = preprocess_exog(exog=exog, return_values=False)
        if not (exog_index[:len(y_index)] == y_index).all():
            raise ValueError(
                ("Different index for `y` and `exog`. They must be equal "
                 "to ensure the correct alignment of values.")
            )

    X_train, y_train = self._create_lags(y=y_values)
    X_train_col_names = [f"lag_{i}" for i in self.lags]
    X_train = pd.DataFrame(
                  data    = X_train,
                  columns = X_train_col_names,
                  index   = y_index[self.max_lag: ]
              )

    if exog is not None:
        # The first `self.max_lag` positions have to be removed from exog
        # since they are not in X_train.
        exog_to_train = exog.iloc[self.max_lag:, ]
        X_train = pd.concat((X_train, exog_to_train), axis=1)

    self.X_train_col_names = X_train.columns.to_list()
    y_train = pd.Series(
                  data  = y_train,
                  index = y_index[self.max_lag: ],
                  name  = 'y'
              )

    return X_train, y_train

create_sample_weights(X_train)

Crate 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\ForecasterAutoreg\ForecasterAutoreg.py

def create_sample_weights(
    self,
    X_train: pd.DataFrame,
)-> np.ndarray:
    """
    Crate 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(y, exog=None, store_in_sample_residuals=True)

Training Forecaster.

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

Parameters:

Name	Type	Description	Default
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_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting.	`True`

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def fit(
    self,
    y: pd.Series,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    store_in_sample_residuals: bool=True
) -> None:
    """
    Training Forecaster.

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

    Parameters
    ----------
    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_in_sample_residuals : bool, default `True`
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting.

    Returns
    -------
    None

    """

    # Reset values in case the forecaster has already been fitted.
    self.index_type          = None
    self.index_freq          = None
    self.last_window         = None
    self.included_exog       = False
    self.exog_type           = None
    self.exog_dtypes         = None
    self.exog_col_names      = None
    self.X_train_col_names   = None
    self.in_sample_residuals = None
    self.fitted              = False
    self.training_range      = None

    if exog is not None:
        self.included_exog = True
        self.exog_type = type(exog)
        self.exog_col_names = \
             exog.columns.to_list() if isinstance(exog, pd.DataFrame) else exog.name

    X_train, y_train = 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.regressor.fit(X=X_train, y=y_train, sample_weight=sample_weight,
                           **self.fit_kwargs)
    else:
        self.regressor.fit(X=X_train, y=y_train, **self.fit_kwargs)

    self.fitted = True
    self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.training_range = preprocess_y(y=y, return_values=False)[1][[0, -1]]
    self.index_type = type(X_train.index)
    if isinstance(X_train.index, pd.DatetimeIndex):
        self.index_freq = X_train.index.freqstr
    else: 
        self.index_freq = X_train.index.step

    # This is done to save time during fit in functions such as backtesting()
    if store_in_sample_residuals:

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

        if len(residuals) > 1000:
            # Only up to 1000 residuals are stored
            rng = np.random.default_rng(seed=123)
            residuals = rng.choice(
                            a       = residuals, 
                            size    = 1000, 
                            replace = False
                        )

        self.in_sample_residuals = residuals

    # The last time window of training data is stored so that lags needed as
    # predictors in the first iteration of `predict()` can be calculated.
    self.last_window = y.iloc[-self.max_lag:].copy()

_recursive_predict(steps, last_window, exog=None)

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 future steps predicted.	required
last_window	numpy ndarray	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1).	required
exog	numpy ndarray	Exogenous variable/s included as predictor/s.	`None`

Returns:

Name	Type	Description
predictions	numpy ndarray	Predicted values.

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def _recursive_predict(
    self,
    steps: int,
    last_window: np.ndarray,
    exog: Optional[np.ndarray]=None
) -> 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 future steps predicted.
    last_window : numpy ndarray
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
    exog : numpy ndarray, default `None`
        Exogenous variable/s included as predictor/s.

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

    """

    predictions = np.full(shape=steps, fill_value=np.nan)

    for i in range(steps):
        X = last_window[-self.lags].reshape(1, -1)
        if exog is not None:
            X = np.column_stack((X, exog[i, ].reshape(1, -1)))
        with warnings.catch_warnings():
            # Suppress scikit-learn warning: "X does not have valid feature names,
            # but NoOpTransformer was fitted with feature names".
            warnings.simplefilter("ignore")
            prediction = self.regressor.predict(X)
            predictions[i] = prediction.ravel()[0]

        # Update `last_window` values. The first position is discarded and 
        # the new prediction is added at the end.
        last_window = np.append(last_window[1:], prediction)

    return predictions

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

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	Number of future steps predicted.	required
last_window	pandas Series	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`

Returns:

Name	Type	Description
predictions	pandas Series	Predicted values.

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def predict(
    self,
    steps: int,
    last_window: Optional[pd.Series]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> 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
        Number of future steps predicted.
    last_window : pandas Series, 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.

    Returns
    -------
    predictions : pandas Series
        Predicted values.

    """

    if last_window is None:
        last_window = copy(self.last_window)

    check_predict_input(
        forecaster_name  = type(self).__name__,
        steps            = steps,
        fitted           = self.fitted,
        included_exog    = self.included_exog,
        index_type       = self.index_type,
        index_freq       = self.index_freq,
        window_size      = self.window_size,
        last_window      = last_window,
        last_window_exog = None,
        exog             = exog,
        exog_type        = self.exog_type,
        exog_col_names   = self.exog_col_names,
        interval         = None,
        alpha            = None,
        max_steps        = None,
        levels           = None,
        series_col_names = None
    ) 

    if exog is not None:
        if isinstance(exog, pd.DataFrame):
            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        else:
            exog = transform_series(
                       series            = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        check_exog_dtypes(exog=exog)
        exog_values = exog.to_numpy()[:steps]
    else:
        exog_values = None

    last_window = transform_series(
                      series            = last_window,
                      transformer       = self.transformer_y,
                      fit               = False,
                      inverse_transform = False
                  )
    last_window_values, last_window_index = preprocess_last_window(
                                                last_window = last_window
                                            )

    predictions = self._recursive_predict(
                      steps       = steps,
                      last_window = copy(last_window_values),
                      exog        = copy(exog_values)
                  )

    predictions = pd.Series(
                      data  = predictions,
                      index = expand_index(
                                  index = last_window_index,
                                  steps = steps
                              ),
                      name = 'pred'
                  )

    predictions = transform_series(
                      series            = predictions,
                      transformer       = self.transformer_y,
                      fit               = False,
                      inverse_transform = True
                  )

    return predictions

predict_bootstrapping(steps, last_window=None, exog=None, n_boot=500, random_state=123, in_sample_residuals=True)

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 Notes section for more information.

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
last_window	pandas Series	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 used to estimate prediction intervals.	`500`
random_state	int	Sets a seed to the random generator, so that boot intervals are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create prediction intervals. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def predict_bootstrapping(
    self,
    steps: int,
    last_window: Optional[pd.Series]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True
) -> 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 Notes section for more information. 

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    last_window : pandas Series, 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 `500`
        Number of bootstrapping iterations used to estimate prediction
        intervals.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot intervals are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create prediction intervals. If `False`, out of
        sample residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).

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

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

    """

    if not in_sample_residuals and self.out_sample_residuals is None:
        raise ValueError(
            ("`forecaster.out_sample_residuals` is `None`. Use "
             "`in_sample_residuals=True` or method `set_out_sample_residuals()` "
             "before `predict_interval()`, `predict_bootstrapping()` or "
             "`predict_dist()`.")
        )

    if last_window is None:
        last_window = copy(self.last_window)

    check_predict_input(
        forecaster_name  = type(self).__name__,
        steps            = steps,
        fitted           = self.fitted,
        included_exog    = self.included_exog,
        index_type       = self.index_type,
        index_freq       = self.index_freq,
        window_size      = self.window_size,
        last_window      = last_window,
        last_window_exog = None,
        exog             = exog,
        exog_type        = self.exog_type,
        exog_col_names   = self.exog_col_names,
        interval         = None,
        alpha            = None,
        max_steps        = None,
        levels           = None,
        series_col_names = None
    )

    if exog is not None:
        if isinstance(exog, pd.DataFrame):
            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        else:
            exog = transform_series(
                       series            = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        exog_values = exog.to_numpy()[:steps]
    else:
        exog_values = None

    last_window = transform_series(
                      series            = last_window,
                      transformer       = self.transformer_y,
                      fit               = False,
                      inverse_transform = False
                  )
    last_window_values, last_window_index = preprocess_last_window(
                                                last_window = last_window
                                            )

    boot_predictions = np.full(
                           shape      = (steps, n_boot),
                           fill_value = np.nan,
                           dtype      = float
                       )
    rng = np.random.default_rng(seed=random_state)
    seeds = rng.integers(low=0, high=10000, size=n_boot)

    if in_sample_residuals:
        residuals = self.in_sample_residuals
    else:
        residuals = self.out_sample_residuals

    for i in range(n_boot):
        # In each bootstraping iteration the initial last_window and exog 
        # need to be restored.
        last_window_boot = last_window_values.copy()
        exog_boot = exog_values.copy() if exog is not None else None

        rng = np.random.default_rng(seed=seeds[i])
        sample_residuals = rng.choice(
                               a       = residuals,
                               size    = steps,
                               replace = True
                           )

        for step in range(steps):

            prediction = self._recursive_predict(
                             steps       = 1,
                             last_window = last_window_boot,
                             exog        = exog_boot 
                         )

            prediction_with_residual  = prediction + sample_residuals[step]
            boot_predictions[step, i] = prediction_with_residual

            last_window_boot = np.append(
                                   last_window_boot[1:],
                                   prediction_with_residual
                               )

            if exog is not None:
                exog_boot = exog_boot[1:]

    boot_predictions = pd.DataFrame(
                           data    = boot_predictions,
                           index   = expand_index(last_window_index, steps=steps),
                           columns = [f"pred_boot_{i}" for i in range(n_boot)]
                       )

    if self.transformer_y:
        for col in boot_predictions.columns:
            boot_predictions[col] = transform_series(
                                        series            = boot_predictions[col],
                                        transformer       = self.transformer_y,
                                        fit               = False,
                                        inverse_transform = True
                                    )

    return boot_predictions

predict_interval(steps, last_window=None, exog=None, interval=[5, 95], n_boot=500, random_state=123, in_sample_residuals=True)

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
last_window	pandas Series	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`
interval	list	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5].	`[5, 95]`
n_boot	int	Number of bootstrapping iterations used to estimate prediction intervals.	`500`
random_state	int	Sets a seed to the random generator, so that boot intervals are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create prediction intervals. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`

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.

Notes

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

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def predict_interval(
    self,
    steps: int,
    last_window: Optional[pd.Series]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    interval: list=[5, 95],
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True
) -> pd.DataFrame:
    """
    Iterative process in which each prediction is used as a predictor
    for the next step, and bootstrapping is used to estimate prediction
    intervals. Both predictions and intervals are returned.

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    last_window : pandas Series, 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.
    interval : list, default `[5, 95]`
        Confidence of the prediction interval estimated. Sequence of 
        percentiles to compute, which must be between 0 and 100 inclusive. 
        For example, interval of 95% should be as `interval = [2.5, 97.5]`.
    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate prediction
        intervals.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot intervals are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create prediction intervals. If `False`, out of
        sample residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).

    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.

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

    """

    check_interval(interval=interval)

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

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

    interval = np.array(interval)/100
    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)

    return predictions

predict_dist(steps, distribution, last_window=None, exog=None, n_boot=500, random_state=123, in_sample_residuals=True)

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
distribution	Object	A distribution object from scipy.stats.	required
last_window	pandas Series	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 used to estimate prediction intervals.	`500`
random_state	int	Sets a seed to the random generator, so that boot intervals are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create prediction intervals. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`

Returns:

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

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def predict_dist(
    self,
    steps: int,
    distribution: object,
    last_window: Optional[pd.Series]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True
) -> pd.DataFrame:
    """
    Fit a given probability distribution for each step. After generating 
    multiple forecasting predictions through a bootstrapping process, each 
    step is fitted to the given distribution.

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    distribution : Object
        A distribution object from scipy.stats.
    last_window : pandas Series, 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 `500`
        Number of bootstrapping iterations used to estimate prediction
        intervals.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot intervals are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create prediction intervals. If `False`, out of
        sample residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).

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

    """

    boot_samples = self.predict_bootstrapping(
                       steps               = steps,
                       last_window         = last_window,
                       exog                = exog,
                       n_boot              = n_boot,
                       random_state        = random_state,
                       in_sample_residuals = in_sample_residuals
                   )       

    param_names = [p for p in inspect.signature(distribution._pdf).parameters
                   if not p=='x'] + ["loc","scale"]
    param_values = np.apply_along_axis(
                        lambda x: distribution.fit(x),
                        axis = 1,
                        arr  = boot_samples
                   )
    predictions = pd.DataFrame(
                      data    = param_values,
                      columns = param_names,
                      index   = boot_samples.index
                  )

    return predictions

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\ForecasterAutoreg\ForecasterAutoreg.py

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

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

    Returns
    -------
    None

    """

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

set_fit_kwargs(fit_kwargs)

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

Parameters:

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

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

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

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

    Returns
    -------
    None

    """

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

set_lags(lags)

Set new value to the attribute lags. Attributes 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.	required

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

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

    Parameters
    ----------
    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.

    Returns
    -------
    None

    """

    self.lags = initialize_lags(type(self).__name__, lags)
    self.max_lag = max(self.lags)
    self.window_size = max(self.lags)

set_out_sample_residuals(residuals, append=True, transform=True, random_state=123)

Set new values to the attribute out_sample_residuals. Out of sample residuals are meant to be calculated using observations that did not participate in the training process.

Parameters:

Name	Type	Description	Default
residuals	numpy ndarray	Values of residuals. If len(residuals) > 1000, only a random sample of 1000 values are stored.	required
append	bool	If True, new residuals are added to the once already stored in the attribute out_sample_residuals. Once the limit of 1000 values is reached, no more values are appended. If False, out_sample_residuals is overwritten with the new residuals.	`True`
transform	bool	If True, new residuals are transformed using self.transformer_y.	`True`
random_state	int	Sets a seed to the random sampling for reproducible output.	`123`

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

def set_out_sample_residuals(
    self, 
    residuals: np.ndarray, 
    append: bool=True,
    transform: bool=True,
    random_state: int=123
)-> None:
    """
    Set new values to the attribute `out_sample_residuals`. Out of sample
    residuals are meant to be calculated using observations that did not
    participate in the training process.

    Parameters
    ----------
    residuals : numpy ndarray
        Values of residuals. If len(residuals) > 1000, only a random sample
        of 1000 values are stored.
    append : bool, default `True`
        If `True`, new residuals are added to the once already stored in the
        attribute `out_sample_residuals`. Once the limit of 1000 values is
        reached, no more values are appended. If False, `out_sample_residuals`
        is overwritten with the new residuals.
    transform : bool, default `True`
        If `True`, new residuals are transformed using self.transformer_y.
    random_state : int, default `123`
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    None

    """

    if not isinstance(residuals, np.ndarray):
        raise TypeError(
            f"`residuals` argument must be `numpy ndarray`. Got {type(residuals)}."
        )

    if not transform and self.transformer_y is not None:
        warnings.warn(
            (f"Argument `transform` is set to `False` but forecaster was trained "
             f"using a transformer {self.transformer_y}. Ensure that the new residuals "
             f"are already transformed or set `transform=True`.")
        )

    if transform and self.transformer_y is not None:
        warnings.warn(
            (f"Residuals will be transformed using the same transformer used "
             f"when training the forecaster ({self.transformer_y}). Ensure that the "
             f"new residuals are on the same scale as the original time series.")
        )

        residuals = transform_series(
                        series            = pd.Series(residuals, name='residuals'),
                        transformer       = self.transformer_y,
                        fit               = False,
                        inverse_transform = False
                    ).to_numpy()

    if len(residuals) > 1000:
        rng = np.random.default_rng(seed=random_state)
        residuals = rng.choice(a=residuals, size=1000, replace=False)

    if append and self.out_sample_residuals is not None:
        free_space = max(0, 1000 - len(self.out_sample_residuals))
        if len(residuals) < free_space:
            residuals = np.hstack((
                            self.out_sample_residuals,
                            residuals
                        ))
        else:
            residuals = np.hstack((
                            self.out_sample_residuals,
                            residuals[:free_space]
                        ))

    self.out_sample_residuals = residuals

get_feature_importances()

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

Parameters:

Name	Type	Description	Default
self			required

Returns:

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

Source code in skforecast\ForecasterAutoreg\ForecasterAutoreg.py

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

    Parameters
    ----------
    self

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

    """

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

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

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

    if feature_importances is not None:
        feature_importances = pd.DataFrame({
                                  'feature': self.X_train_col_names,
                                  'importance': feature_importances
                              })

    return feature_importances