ForecasterAutoregMultiSeries

ForecasterAutoregMultiSeries(regressor, lags, encoding='ordinal_category', transformer_series=StandardScaler(), transformer_exog=None, weight_func=None, series_weights=None, differentiation=None, dropna_from_series=False, fit_kwargs=None, forecaster_id=None)

Bases: ForecasterBase

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

Parameters:

Name	Type	Description	Default
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API.	required
lags	int, list, numpy ndarray, range	Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1. int: include lags from 1 to lags (included). list, 1d numpy ndarray or range: include only lags present in lags, all elements must be int.	required
encoding	str	Encoding used to identify the different series. If 'ordinal', a single column is created with integer values from 0 to n_series - 1. If 'ordinal_category', a single column is created with integer values from 0 to n_series - 1 and the column is transformed into pandas.category dtype so that it can be used as a categorical variable. If 'onehot', a binary column is created for each series. New in version 0.12.0	`'ordinal_category'`
transformer_series	(transformer(preprocessor), dict)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. Transformation is applied to each series before training the forecaster. ColumnTransformers are not allowed since they do not have inverse_transform method. If single transformer: it is cloned and applied to all series. If dict of transformers: a different transformer can be used for each series.	`sklearn.preprocessing.StandardScaler`
transformer_exog	transformer	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API. The transformation is applied to exog before training the forecaster. inverse_transform is not available when using ColumnTransformers.	`None`
weight_func	(Callable, dict)	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. See Notes section for more details on the use of the weights. If single function: it is applied to all series. If dict {'series_column_name' : Callable}: a different function can be used for each series, a weight of 1 is given to all series not present in weight_func.	`None`
series_weights	dict	Weights associated with each series {'series_column_name' : float}. It is only applied if the regressor used accepts sample_weight in its fit method. See Notes section for more details on the use of the weights. If a dict is provided, a weight of 1 is given to all series not present in series_weights. If None, all levels have the same weight.	`None`
differentiation	int	Order of differencing applied to the time series before training the forecaster. If None, no differencing is applied. The order of differentiation is the number of times the differencing operation is applied to a time series. Differencing involves computing the differences between consecutive data points in the series. Differentiation is reversed in the output of predict() and predict_interval(). WARNING: This argument is newly introduced and requires special attention. It is still experimental and may undergo changes. New in version 0.12.0	`None`
dropna_from_series	bool	Determine whether NaN detected in the training matrices will be dropped. If True, drop NaNs in X_train and same rows in y_train. If False, leave NaNs in X_train and warn the user. New in version 0.12.0	`False`
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.	`None`
forecaster_id	(str, int)	Name used as an identifier of the forecaster.	`None`

Attributes:

Name	Type	Description
regressor	regressor or pipeline compatible with the scikit-learn API	An instance of a regressor or pipeline compatible with the scikit-learn API.
lags	numpy ndarray	Lags used as predictors.
encoding	str	Encoding used to identify the different series. If 'ordinal', a single column is created with integer values from 0 to n_series - 1. If 'ordinal_category', a single column is created with integer values from 0 to n_series - 1 and the column is transformed into pandas.category dtype so that it can be used as a categorical variable. If 'onehot', a binary column is created for each series. New in version 0.12.0
encoder	preprocessing	Scikit-learn preprocessing encoder used to encode the series. New in version 0.12.0
encoding_mapping	dict	Mapping of the encoding used to identify the different series.
transformer_series	(transformer(preprocessor), dict)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API with methods: fit, transform, fit_transform and inverse_transform. Transformation is applied to each series before training the forecaster. ColumnTransformers are not allowed since they do not have inverse_transform method. If single transformer: it is cloned and applied to all series. If dict of transformers: a different transformer can be used for each series.
transformer_series_	dict	Dictionary with the transformer for each series. It is created cloning the objects in transformer_series and is used internally to avoid overwriting.
transformer_exog	transformer(preprocessor)	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API. The transformation is applied to exog before training the forecaster. inverse_transform is not available when using ColumnTransformers.
weight_func	(Callable, dict)	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. See Notes section for more details on the use of the weights. If single function: it is applied to all series. If dict {'series_column_name' : Callable}: a different function can be used for each series, a weight of 1 is given to all series not present in weight_func.
weight_func_	dict	Dictionary with the weight_func for each series. It is created cloning the objects in weight_func and is used internally to avoid overwriting.
source_code_weight_func	(str, dict)	Source code of the custom function(s) used to create weights.
series_weights	dict	Weights associated with each series {'series_column_name' : float}. It is only applied if the regressor used accepts sample_weight in its fit method. See Notes section for more details on the use of the weights. If a dict is provided, a weight of 1 is given to all series not present in series_weights. If None, all levels have the same weight.
series_weights_	dict	Weights associated with each series.It is created as a clone of series_weights and is used internally to avoid overwriting.
differentiation	int	Order of differencing applied to the time series before training the forecaster.
differentiator	TimeSeriesDifferentiator	Skforecast object used to differentiate the time series.
differentiator_	dict	Dictionary with the differentiator for each series. It is created cloning the objects in differentiator and is used internally to avoid overwriting.
dropna_from_series	bool	Determine whether NaN detected in the training matrices will be dropped.
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.
window_size_diff	int	Size of the window extended by the order of differentiation. When using differentiation, the window_size is increased by the order of differentiation so that the predictors can be created correctly.
last_window	dict	Last window of training data for each series. It stores the values needed to predict the next step immediately after the training data.
index_type	type	Type of index of the input used in training.
index_freq	str	Frequency of Index of the input used in training.
training_range	dict	First and last values of index of the data used during training for each series.
series_col_names	list	Names of the series (levels) provided by the user during training.
series_X_train	list	Names of the series (levels) included in the matrix X_train created internally for training. It can be different from series_col_names if some series are dropped during the training process because of NaNs or because they are not present in the training period.
X_train_col_names	list	Names of columns of the matrix created internally for training.
included_exog	bool	If the forecaster has been trained using exogenous variable/s.
exog_type	type	Type of exogenous variable/s used in training.
exog_dtypes	dict	Type of each exogenous variable/s used in training. If transformer_exog is used, the dtypes are calculated before the transformation.
exog_col_names	list	Names of the exogenous variables used during training.
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.
in_sample_residuals	dict	Residuals of the model when predicting training data. Only stored up to 1000 values in the form {level: residuals}. If transformer_series is not None, residuals are stored in the transformed scale.
out_sample_residuals	dict	Residuals of the model when predicting non-training data. Only stored up to 1000 values in the form {level: residuals}. If transformer_series is not None, residuals are assumed to be in the transformed scale. Use set_out_sample_residuals() method to set values.
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.
skforecast_version	str	Version of skforecast library used to create the forecaster.
python_version	str	Version of python used to create the forecaster.
forecaster_id	(str, int)	Name used as an identifier of the forecaster.

Notes

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

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def __init__(
    self,
    regressor: object,
    lags: Union[int, np.ndarray, list],
    encoding: str='ordinal_category',
    transformer_series: Optional[Union[object, dict]]=StandardScaler(),
    transformer_exog: Optional[object]=None,
    weight_func: Optional[Union[Callable, dict]]=None,
    series_weights: Optional[dict]=None,
    differentiation: Optional[int]=None,
    dropna_from_series: bool=False,
    fit_kwargs: Optional[dict]=None,
    forecaster_id: Optional[Union[str, int]]=None
) -> None:

    self.regressor               = regressor
    self.encoding                = encoding
    self.encoder                 = None
    self.encoding_mapping        = {}
    self.transformer_series      = transformer_series
    self.transformer_series_     = None
    self.transformer_exog        = transformer_exog
    self.weight_func             = weight_func
    self.weight_func_            = None
    self.source_code_weight_func = None
    self.series_weights          = series_weights
    self.series_weights_         = None
    self.differentiation         = differentiation
    self.differentiator          = None
    self.differentiator_         = None
    self.dropna_from_series      = dropna_from_series
    self.last_window             = None
    self.index_type              = None
    self.index_freq              = None
    self.training_range          = None
    self.series_col_names        = None
    self.series_X_train          = None
    self.X_train_col_names       = None
    self.included_exog           = False
    self.exog_type               = None
    self.exog_dtypes             = None
    self.exog_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.skforecast_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.window_size_diff = self.max_lag

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

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

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

    if self.encoding not in ['ordinal', 'ordinal_category', 'onehot']:
        raise ValueError(
            (f"Argument `encoding` must be one of the following values: 'ordinal', "
             f"'ordinal_category', 'onehot'. Got '{self.encoding}'.")
        )

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

_create_lags(y, series_name)

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
series_name	str	Name of the 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\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def _create_lags(
    self, 
    y: np.ndarray, 
    series_name: str
) -> 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.
    series_name : str
        Name of the 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 '{series_name}', ({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_single_series(y, ignore_exog, exog=None)

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

Parameters:

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

Returns:

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

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

    """

    series_name = y.name
    fit_transformer = False if self.fitted else True
    y = transform_series(
            series            = y,
            transformer       = self.transformer_series_[series_name],
            fit               = fit_transformer,
            inverse_transform = False
        )

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

    if self.differentiation is not None:
        if not self.fitted:
            y_values = self.differentiator_[series_name].fit_transform(y_values)
        else:
            differentiator = clone(self.differentiator_[series_name])
            y_values = differentiator.fit_transform(y_values)

    X_train, y_train = self._create_lags(y=y_values, series_name=series_name)

    X_train_lags = pd.DataFrame(
                       data    = X_train,
                       columns = [f"lag_{i}" for i in self.lags],
                       index   = y_index[self.max_lag: ]
                   )
    X_train_lags['_level_skforecast'] = series_name

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

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

    if self.differentiation is not None:
        X_train_lags = X_train_lags.iloc[self.differentiation: ]
        y_train = y_train.iloc[self.differentiation: ]
        if X_train_exog is not None:
            X_train_exog = X_train_exog.iloc[self.differentiation: ]

    return X_train_lags, X_train_exog, y_train

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

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

Parameters:

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

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

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

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

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

    """

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

    if self.fitted and not (series_col_names == self.series_col_names):
        raise ValueError(
            (f"Once the Forecaster has been trained, `series` must have the "
             f"same columns as the series used during training:\n" 
             f" Got      : {series_col_names}\n"
             f" Expected : {self.series_col_names}")
        )

    exog_dict = {serie: None for serie in series_col_names}
    exog_col_names = None
    if exog is not None:
        exog_dict, exog_col_names = check_preprocess_exog_multiseries(
                                        input_series_is_dict = input_series_is_dict,
                                        series_indexes       = series_indexes,
                                        series_col_names     = series_col_names,
                                        exog                 = exog,
                                        exog_dict            = exog_dict
                                    )

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

    if not self.fitted:
        self.transformer_series_ = initialize_transformer_series(
                                       series_col_names = series_col_names,
                                       transformer_series = self.transformer_series
                                   )

    if self.differentiation is None:
        self.differentiator_ = {serie: None for serie in series_col_names}
    else:
        if not self.fitted:
            self.differentiator_ = {serie: clone(self.differentiator) 
                                    for serie in series_col_names}

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

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

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

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

        X_train_lags_buffer.append(X_train_lags)
        X_train_exog_buffer.append(X_train_exog)
        y_train_buffer.append(y_train)
    # ======================================================================

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

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

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

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

    del encoded_values

    exog_dtypes = None
    if exog is not None:

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

        exog_col_names = X_train_exog.columns.to_list()
        exog_dtypes = get_exog_dtypes(exog=X_train_exog)

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

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

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

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

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

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

    if self.encoding == 'onehot':
        series_X_train = [
            col for col in series_col_names if X_train[col].sum() > 0
        ]
    else:
        series_X_train = [
            k for k, v in self.encoding_mapping.items()
            if v in X_train['_level_skforecast'].unique()
        ]

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

        series_to_store = (
            series_X_train if store_last_window is True else store_last_window
        )

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

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

    return (
        X_train,
        y_train,
        series_indexes,
        series_col_names,
        series_X_train,
        exog_col_names,
        exog_dtypes,
        last_window,
    )

create_train_X_y(series, exog=None)

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

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

    Parameters
    ----------
    series : pandas DataFrame, dict
        Training time series.
    exog : pandas Series, pandas DataFrame, dict, default `None`
        Exogenous variable/s included as predictor/s.

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

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

    """

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

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

    return X_train, y_train

create_sample_weights(series_col_names, X_train)

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

Parameters:

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

Returns:

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

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

    """

    weights = None
    weights_samples = None
    weights_series = None

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

        if self.encoding == "onehot":
            weights_series = [
                np.repeat(self.series_weights_[serie], sum(X_train[serie]))
                for serie in series_col_names
            ]
        else:
            weights_series = [
                np.repeat(
                    self.series_weights_[serie],
                    sum(X_train["_level_skforecast"] == self.encoding_mapping[serie]),
                )
                for serie in series_col_names
            ]

        weights_series = np.concatenate(weights_series)

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

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

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

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

    return weights

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

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

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

Parameters:

Name	Type	Description	Default
series	pandas DataFrame, dict	Training time series.	required
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`
store_last_window	(bool, list)	Whether or not to store the last window of training data. If True, last_window is stored for all series. If list, last_window is stored for the series present in the list. If False, last_window is not stored.	`True`
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting.	`True`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the training process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`

Returns:

Type	Description
None

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

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

        - If `True`, last_window is stored for all series. 
        - If `list`, last_window is stored for the series present in the list.
        - If `False`, last_window is not stored.
    store_in_sample_residuals : bool, default `True`
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting.
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the training 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    None

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

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

    (
        X_train,
        y_train,
        series_indexes,
        series_col_names,
        series_X_train,
        exog_col_names,
        exog_dtypes,
        last_window
    ) = self._create_train_X_y(
            series=series, exog=exog, store_last_window=store_last_window
    )

    sample_weight = self.create_sample_weights(
                        series_col_names = series_col_names,
                        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.series_col_names = series_col_names
    self.series_X_train = series_X_train
    self.X_train_col_names = X_train.columns.to_list()
    self.fitted = True
    self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.training_range = {k: v[[0, -1]] for k, v in series_indexes.items()}
    self.index_type = type(series_indexes[series_col_names[0]])
    if isinstance(series_indexes[series_col_names[0]], pd.DatetimeIndex):
        self.index_freq = series_indexes[series_col_names[0]].freqstr
    else: 
        self.index_freq = series_indexes[series_col_names[0]].step

    if exog is not None:
        self.included_exog = True
        self.exog_type = type(exog)
        self.exog_col_names = exog_col_names
        self.exog_dtypes = exog_dtypes

    in_sample_residuals = {}
    if store_in_sample_residuals:

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

        for col in series_X_train:
            if self.encoding == 'onehot':
                in_sample_residuals[col] = residuals.loc[X_train[col] == 1.].to_numpy()
            else:
                encoded_value = self.encoding_mapping[col]
                in_sample_residuals[col] = (
                    residuals.loc[X_train['_level_skforecast'] == encoded_value].to_numpy()
                )
            if len(in_sample_residuals[col]) > 1000:
                # Only up to 1000 residuals are stored
                rng = np.random.default_rng(seed=123)
                in_sample_residuals[col] = rng.choice(
                                               a       = in_sample_residuals[col], 
                                               size    = 1000, 
                                               replace = False
                                           )
    else:
        for col in series_X_train:
            in_sample_residuals[col] = None

    self.in_sample_residuals = in_sample_residuals

    if store_last_window:
        self.last_window = last_window

    set_skforecast_warnings(suppress_warnings, action='default')

_recursive_predict(steps, level, 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
level	str	Time series to be 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\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def _recursive_predict(
    self,
    steps: int,
    level: str,
    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.
    level : str
        Time series to be 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)
    level_encoded = np.array([self.encoding_mapping[level]], dtype='float64')

    for i in range(steps):

        X = last_window[-self.lags].reshape(1, -1)

        if self.encoding == 'onehot':
            levels_dummies = np.zeros(shape=(1, len(self.series_col_names)), dtype=float)
            levels_dummies[0][self.series_col_names.index(level)] = 1.
            X = np.column_stack((X, levels_dummies.reshape(1, -1)))
        else:
            X = np.column_stack((X, level_encoded))

        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, levels=None, last_window=None, exog=None, suppress_warnings=False)

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

Parameters:

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

Returns:

Name	Type	Description
predictions	pandas DataFrame	Predicted values, one column for each level.

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

    Returns
    -------
    predictions : pandas DataFrame
        Predicted values, one column for each level.

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    input_levels_is_list = False
    if levels is None:
        levels = self.series_X_train
    elif isinstance(levels, str):
        levels = [levels]
    else:
        input_levels_is_list = True

    if last_window is None and self.fitted:
        available_last_windows = set() if self.last_window is None else set(self.last_window.keys())
        not_available_last_window = set(levels) - available_last_windows
        if not_available_last_window:
            warnings.warn(
                (f"Levels {not_available_last_window} are excluded from "
                 f"prediction since they were not stored in `last_window` "
                 f"attribute during training. If you don't want to retrain "
                 f"the Forecaster, provide `last_window` as argument."),
                IgnoredArgumentWarning
            )
            levels = [level for level in levels 
                      if level not in not_available_last_window]

            if not levels:
                raise ValueError(
                    ("No series to predict. None of the series are present in "
                     "`last_window` attribute. Provide `last_window` as argument "
                     "in predict method.")
                )

        last_index_levels = [
            v.index[-1] 
            for k, v in self.last_window.items()
            if k in levels
        ]
        if len(set(last_index_levels)) > 1:
            max_index_levels = max(last_index_levels)
            selected_levels = [
                k
                for k, v in self.last_window.items()
                if k in levels and v.index[-1] == max_index_levels
            ]

            series_excluded_from_last_window = set(levels) - set(selected_levels)
            levels = selected_levels

            if input_levels_is_list and series_excluded_from_last_window:
                warnings.warn(
                    (f"Only series whose last window ends at the same index "
                     f"can be predicted together. Series that do not reach "
                     f"the maximum index, '{max_index_levels}', are excluded "
                     f"from prediction: {series_excluded_from_last_window}."),
                    IgnoredArgumentWarning
                )

        last_window = pd.DataFrame(
            {k: v 
             for k, v in self.last_window.items() 
             if k in levels}
        )

    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_diff,
        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           = levels,
        series_col_names = self.series_col_names
    )

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

    if exog is not None:
        if isinstance(exog, (pd.Series, pd.DataFrame)):
            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:
            # Empty dataframe to be filled with the exog values of each level
            empty_exog = pd.DataFrame(
                             data    = np.nan,
                             columns = self.exog_col_names,
                             index   = prediction_index
                         )
    else:
        exog_values = None

    predictions = []
    for level in levels:

        last_window_level = transform_series(
                                series            = last_window[level],
                                transformer       = self.transformer_series_[level],
                                fit               = False,
                                inverse_transform = False
                            )
        last_window_values = last_window_level.to_numpy()
        if self.differentiation is not None:
            last_window_values = self.differentiator_[level].fit_transform(last_window_values)

        if isinstance(exog, dict):
            # Fill the empty dataframe with the exog values of each level
            # and transform them if necessary
            exog_level = exog[level]
            if isinstance(exog_level, pd.Series):
                exog_level = exog_level.to_frame()

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

            check_exog_dtypes(
                exog      = exog_level,
                series_id = f"`exog` for series '{level}'"
            )
            exog_values = exog_level.to_numpy()

        preds_level = self._recursive_predict(
                          steps       = steps,
                          level       = level,
                          last_window = last_window_values,
                          exog        = exog_values
                      )

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

        preds_level = pd.Series(
                          data  = preds_level,
                          index = prediction_index,
                          name  = level
                      )

        preds_level = transform_series(
                          series            = preds_level,
                          transformer       = self.transformer_series_[level],
                          fit               = False,
                          inverse_transform = True
                      )

        predictions.append(preds_level)

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

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

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	`None`
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`
n_boot	int	Number of bootstrapping iterations used to estimate predictions.	`500`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`

Returns:

Name	Type	Description
boot_predictions	dict	Predictions generated by bootstrapping for each level. {level: pandas DataFrame, shape (steps, n_boot)}

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def predict_bootstrapping(
    self,
    steps: int,
    levels: Optional[Union[str, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    suppress_warnings: bool=False
) -> dict:
    """
    Generate multiple forecasting predictions using a bootstrapping process. 
    By sampling from a collection of past observed errors (the residuals),
    each iteration of bootstrapping generates a different set of predictions. 
    Only levels whose last window ends at the same datetime index can be 
    predicted together. See the Notes section for more information. 

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default `None`
        Exogenous variable/s included as predictor/s.
    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate predictions.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot predictions are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. If `False`, out of sample 
        residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

    Returns
    -------
    boot_predictions : dict
        Predictions generated by bootstrapping for each level.
        {level: pandas DataFrame, shape (steps, n_boot)}

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    if self.fitted:

        input_levels_is_list = False 
        if levels is None:
            levels = self.series_X_train
        elif isinstance(levels, str):
            levels = [levels]
        else:
            input_levels_is_list = True

        if last_window is None:
            available_last_windows = set() if self.last_window is None else set(self.last_window.keys())
            not_available_last_window = set(levels) - available_last_windows
            if not_available_last_window:
                warnings.warn(
                    (f"Levels {not_available_last_window} are excluded from "
                     f"prediction since they were not stored in `last_window` "
                     f"attribute during training. If you don't want to retrain "
                     f"the Forecaster, provide `last_window` as argument."),
                     IgnoredArgumentWarning
                )
                levels = [level for level in levels 
                          if level not in not_available_last_window]

                if not levels:
                    raise ValueError(
                        ("No series to predict. None of the series are present in "
                         "`last_window` attribute. Provide `last_window` as argument "
                         "in predict method.")
                    )

            last_index_levels = [
                v.index[-1] 
                for k, v in self.last_window.items()
                if k in levels
            ]
            if len(set(last_index_levels)) > 1:
                max_index_levels = max(last_index_levels)
                selected_levels = [
                    k
                    for k, v in self.last_window.items()
                    if k in levels and v.index[-1] == max_index_levels
                ]

                series_excluded_from_last_window = set(levels) - set(selected_levels)
                levels = selected_levels

                if input_levels_is_list and series_excluded_from_last_window:
                    warnings.warn(
                        (f"Only series whose last window ends at the same index "
                         f"can be predicted together. Series that do not reach "
                         f"the maximum index, '{max_index_levels}', are excluded "
                         f"from prediction: {series_excluded_from_last_window}."),
                         IgnoredArgumentWarning
                    )

            last_window = pd.DataFrame(
                {k: v 
                 for k, v in self.last_window.items() 
                 if k in levels}
            )

        if in_sample_residuals:
            if not set(levels).issubset(set(self.in_sample_residuals.keys())):
                raise ValueError(
                    (f"Not `forecaster.in_sample_residuals` for levels: "
                     f"{set(levels) - set(self.in_sample_residuals.keys())}.")
                )
            residuals_levels = self.in_sample_residuals
        else:
            if 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()`,`predict_quantiles()` or "
                     "`predict_dist()`.")
                )
            else:
                if not set(levels).issubset(set(self.out_sample_residuals.keys())):
                    raise ValueError(
                        (f"Not `forecaster.out_sample_residuals` for levels: "
                         f"{set(levels) - set(self.out_sample_residuals.keys())}. "
                         f"Use method `set_out_sample_residuals()`.")
                    )
            residuals_levels = self.out_sample_residuals

        check_residuals = (
            "forecaster.in_sample_residuals" if in_sample_residuals
            else "forecaster.out_sample_residuals"
        )
        for level in levels:
            if (level not in residuals_levels.keys() or 
                residuals_levels[level] is None or 
                len(residuals_levels[level]) == 0):
                raise ValueError(
                    (f"Not available residuals for level '{level}'. "
                     f"Check `{check_residuals}`.")
                )
            elif (any(element is None for element in residuals_levels[level]) or
                  np.any(np.isnan(residuals_levels[level]))):
                raise ValueError(
                    (f"forecaster residuals for level '{level}' contains `None` "
                     f"or `NaNs` values. Check `{check_residuals}`.")
                )

    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_diff,
        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           = levels,
        series_col_names = self.series_col_names
    )

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

    if exog is not None:
        if isinstance(exog, (pd.Series, pd.DataFrame)):
            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:
            # Empty dataframe to be filled with the exog values of each level
            empty_exog = pd.DataFrame(
                             data    = np.nan,
                             columns = self.exog_col_names,
                             index   = prediction_index
                         )
    else:
        exog_values = None

    boot_predictions = {}
    for level in levels:

        last_window_level = transform_series(
                                series            = last_window[level],
                                transformer       = self.transformer_series_[level],
                                fit               = False,
                                inverse_transform = False
                            )
        last_window_values = last_window_level.to_numpy()
        if self.differentiation is not None:
            last_window_values = self.differentiator_[level].fit_transform(last_window_values)

        if isinstance(exog, dict):
            # Fill the empty dataframe with the exog values of each level
            # and transform them if necessary
            exog_level = exog[level]
            if isinstance(exog_level, pd.Series):
                exog_level = exog_level.to_frame()

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

            check_exog_dtypes(
                exog      = exog_level,
                series_id = f"`exog` for series '{level}'"
            )
            exog_values = exog_level.to_numpy()

        level_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)

        residuals = residuals_levels[level]

        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,
                                 level       = level,
                                 last_window = last_window_boot,
                                 exog        = exog_boot 
                             )

                prediction_with_residual = prediction + sample_residuals[step]
                level_boot_predictions[step, i] = prediction_with_residual[0]

                last_window_boot = np.append(
                                       last_window_boot[1:],
                                       prediction_with_residual
                                   )
                if exog is not None:
                    exog_boot = exog_boot[1:]

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

        level_boot_predictions = pd.DataFrame(
                                     data    = level_boot_predictions,
                                     index   = prediction_index,
                                     columns = [f"pred_boot_{i}" for i in range(n_boot)]
                                 )

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

        boot_predictions[level] = level_boot_predictions

    set_skforecast_warnings(suppress_warnings, action='default')

    return boot_predictions

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

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	`None`
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`
interval	list	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5].	`[5, 95]`
n_boot	int	Number of bootstrapping iterations used to estimate prediction intervals.	`500`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`

Returns:

Name	Type	Description
predictions	pandas DataFrame	Values predicted by the forecaster and their estimated interval. level: predictions. level_lower_bound: lower bound of the interval. level_upper_bound: upper bound of the interval.

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default `None`
        Exogenous variable/s included as predictor/s.
    interval : list, default `[5, 95]`
        Confidence of the prediction interval estimated. Sequence of 
        percentiles to compute, which must be between 0 and 100 inclusive. 
        For example, interval of 95% should be as `interval = [2.5, 97.5]`.
    n_boot : int, default `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 predictions 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 predictions. If `False`, out of sample 
        residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

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

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

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(interval=interval)

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

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

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

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

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

predict_quantiles(steps, levels=None, last_window=None, exog=None, quantiles=[0.05, 0.5, 0.95], n_boot=500, random_state=123, in_sample_residuals=True, suppress_warnings=False)

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	`None`
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`
quantiles	list	Sequence of quantiles to compute, which must be between 0 and 1 inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as quantiles = [0.05, 0.5, 0.95].	`[0.05, 0.5, 0.95]`
n_boot	int	Number of bootstrapping iterations used to estimate quantiles.	`500`
random_state	int	Sets a seed to the random generator, so that boot quantiles are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create quantiles. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def predict_quantiles(
    self,
    steps: int,
    levels: Optional[Union[str, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame, dict]]=None,
    quantiles: list=[0.05, 0.5, 0.95],
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    suppress_warnings: bool=False
) -> pd.DataFrame:
    """
    Calculate the specified quantiles for each step. After generating 
    multiple forecasting predictions through a bootstrapping process, each 
    quantile is calculated for each step.

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default `None`
        Exogenous variable/s included as predictor/s.
    quantiles : list, default `[0.05, 0.5, 0.95]`
        Sequence of quantiles to compute, which must be between 0 and 1 
        inclusive. For example, quantiles of 0.05, 0.5 and 0.95 should be as 
        `quantiles = [0.05, 0.5, 0.95]`.
    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate quantiles.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot quantiles are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create quantiles. If `False`, out of sample 
        residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

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

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(quantiles=quantiles)

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

    predictions = []

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

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

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

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

Parameters:

Name	Type	Description	Default
steps	int	Number of future steps predicted.	required
distribution	Object	A distribution object from scipy.stats. For example scipy.stats.norm.	required
levels	(str, list)	Time series to be predicted. If None all levels whose last window ends at the same datetime index will be predicted together.	`None`
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame, dict	Exogenous variable/s included as predictor/s.	`None`
n_boot	int	Number of bootstrapping iterations used to estimate predictions.	`500`
random_state	int	Sets a seed to the random generator, so that boot predictions are always deterministic.	`123`
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals are used. In the latter case, the user should have calculated and stored the residuals within the forecaster (see set_out_sample_residuals()).	`True`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`

Returns:

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

    Parameters
    ----------
    steps : int
        Number of future steps predicted.
    distribution : Object
        A distribution object from scipy.stats. For example scipy.stats.norm.
    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels whose last window
        ends at the same datetime index will be predicted together.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, dict, default `None`
        Exogenous variable/s included as predictor/s.
    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate predictions.
    random_state : int, default `123`
        Sets a seed to the random generator, so that boot predictions are always 
        deterministic.
    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. If `False`, out of sample 
        residuals are used. In the latter case, the user should have
        calculated and stored the residuals within the forecaster (see
        `set_out_sample_residuals()`).
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

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

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

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

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

        predictions.append(pred_level)

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

set_params(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\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.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\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.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, window_size and window_size_diff 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\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def set_lags(
    self, 
    lags: Union[int, list, np.ndarray, range]
) -> None:
    """
    Set new value to the attribute `lags`. Attributes `max_lag`, 
    `window_size` and  `window_size_diff` 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)
    self.window_size_diff = max(self.lags)
    if self.differentiation is not None:
        self.window_size_diff += self.differentiation  

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	dict	Dictionary of numpy ndarrays with the residuals of each level in the form {level: residuals}. If len(residuals) > 1000, only a random sample of 1000 values are stored. Keys must be the same as levels.	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_series.	`True`
random_state	int	Sets a seed to the random sampling for reproducible output.	`123`

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

def set_out_sample_residuals(
    self, 
    residuals: dict,
    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 : dict
        Dictionary of numpy ndarrays with the residuals of each level in the
        form {level: residuals}. If len(residuals) > 1000, only a random 
        sample of 1000 values are stored. Keys must be the same as `levels`.
    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_series.
    random_state : int, default `123`
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    None

    """

    if not isinstance(residuals, dict) or not all(isinstance(x, np.ndarray) for x in residuals.values()):
        raise TypeError(
            (f"`residuals` argument must be a dict of numpy ndarrays in the form "
             "`{level: residuals}`. " 
             f"Got {type(residuals)}.")
        )

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

    if self.out_sample_residuals is None:
        self.out_sample_residuals = {level: None for level in self.series_col_names}

    if not set(self.out_sample_residuals.keys()).issubset(set(residuals.keys())):
        warnings.warn(
            (
                f"Only residuals of levels " 
                f"{set(self.out_sample_residuals.keys()).intersection(set(residuals.keys()))} "
                f"are updated."
            ), IgnoredArgumentWarning
        )

    residuals = {
        key: value 
        for key, value in residuals.items() 
        if key in self.out_sample_residuals.keys()
    }

    for level, value in residuals.items():

        residuals_level = value

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

        if transform and self.transformer_series_ and self.transformer_series_[level]:
            warnings.warn(
                (f"Residuals will be transformed using the same transformer used "
                 f"when training the forecaster for level {level} : "
                 f"({self.transformer_series_[level]}). Ensure that the new "
                 f"residuals are on the same scale as the original time series.")
            )
            residuals_level = transform_series(
                                  series            = pd.Series(residuals_level, name='residuals'),
                                  transformer       = self.transformer_series_[level],
                                  fit               = False,
                                  inverse_transform = False
                              ).to_numpy()

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

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

        self.out_sample_residuals[level] = residuals_level

get_feature_importances(sort_importance=True)

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

Parameters:

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

Returns:

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

Source code in skforecast\ForecasterAutoregMultiSeries\ForecasterAutoregMultiSeries.py

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

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

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

    """

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

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

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

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

    return feature_importances