ForecasterAutoregMultiVariate

ForecasterAutoregMultiVariate(regressor, level, steps, lags, transformer_series=StandardScaler(), transformer_exog=None, weight_func=None, fit_kwargs=None, n_jobs='auto', forecaster_id=None)

Bases: ForecasterBase

This class turns any regressor compatible with the scikit-learn API into a autoregressive multivariate direct multi-step forecaster. A separate model is created for each forecast time step. See documentation for more details.

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
level	str	Name of the time series to be predicted.	required
steps	int	Maximum number of future steps the forecaster will predict when using method predict(). Since a different model is created for each step, this value must be defined before training.	required
lags	int, list, numpy ndarray, range, dict	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. dict: create different lags for each series. {'series_column_name': lags}.	required
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	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. The resulting sample_weight cannot have negative values.	`None`
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.	`None`
n_jobs	(int, auto)	The number of jobs to run in parallel. If -1, then the number of jobs is set to the number of cores. If 'auto', n_jobs is set using the function skforecast.utils.select_n_jobs_fit_forecaster. New in version 0.9.0	`'auto'`
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. An instance of this regressor is trained for each step. All of them are stored in self.regressors_.
regressors_	dict	Dictionary with regressors trained for each step. They are initialized as a copy of regressor.
steps	int	Number of future steps the forecaster will predict when using method predict(). Since a different model is created for each step, this value should be defined before training.
lags	numpy ndarray, dict	Lags used as predictors.
lags_	dict	Dictionary containing the lags of each series. Created from lags and used internally.
transformer_series	transformer (preprocessor), dict, default `None`	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	An instance of a transformer (preprocessor) compatible with the scikit-learn preprocessing API. The transformation is applied to exog before training the forecaster. inverse_transform is not available when using ColumnTransformers.
weight_func	Callable	Function that defines the individual weights for each sample based on the index. For example, a function that assigns a lower weight to certain dates. Ignored if regressor does not have the argument sample_weight in its fit method. The resulting sample_weight cannot have negative values.
source_code_weight_func	str	Source code of the custom function used to create weights.
max_lag	int	Maximum value of lag included in lags.
window_size	int	Size of the window needed to create the predictors. It is equal to max_lag.
window_size_diff	int	This attribute has the same value as window_size as this Forecaster doesn't support differentiation. Present here for API consistency.
last_window	pandas Series	Last window seen by the forecaster during training. It stores the values needed to predict the next step immediately after the training data.
index_type	type	Type of index of the input used in training.
index_freq	str	Frequency of Index of the input used in training.
training_range	pandas Index	First and last values of index of the data used during training.
included_exog	bool	If the forecaster has been trained using exogenous variable/s.
exog_type	type	Type of exogenous 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 after the transformation.
exog_col_names	list	Names of the exogenous variables used during training.
series_col_names	list	Names of the series used during training.
series_X_train	list	Names of the series added to X_train when creating the training matrices with _create_train_X_y method. It is a subset of series_col_names.
X_train_col_names	list	Names of columns of the matrix created internally for training.
fit_kwargs	dict	Additional arguments to be passed to the fit method of the regressor.
in_sample_residuals	dict	Residuals of the models when predicting training data. Only stored up to 1000 values per model in the form {step: residuals}. If transformer_series is not None, residuals are stored in the transformed scale.
out_sample_residuals	dict	Residuals of the models when predicting non training data. Only stored up to 1000 values per model in the form {step: 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.
n_jobs	int, 'auto', default `'auto'`	The number of jobs to run in parallel. If -1, then the number of jobs is set to the number of cores. If 'auto', n_jobs is set using the fuction skforecast.utils.select_n_jobs_fit_forecaster. New in version 0.9.0
forecaster_id	(str, int)	Name used as an identifier of the forecaster.
dropna_from_series	Ignored	Not used, present here for API consistency by convention.

Notes

A separate model is created for each forecasting time step. It is important to note that all models share the same parameter and hyperparameter configuration.

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def __init__(
    self,
    regressor: object,
    level: str,
    steps: int,
    lags: Union[int, np.ndarray, list, dict],
    transformer_series: Optional[Union[object, dict]]=StandardScaler(),
    transformer_exog: Optional[object]=None,
    weight_func: Optional[Callable]=None,
    fit_kwargs: Optional[dict]=None,
    n_jobs: Union[int, str]='auto',
    forecaster_id: Optional[Union[str, int]]=None
) -> None:

    self.regressor               = regressor
    self.level                   = level
    self.steps                   = steps
    self.transformer_series      = transformer_series
    self.transformer_series_     = None
    self.transformer_exog        = transformer_exog
    self.weight_func             = weight_func
    self.source_code_weight_func = None
    self.max_lag                 = None
    self.window_size             = None
    self.last_window             = None
    self.index_type              = None
    self.index_freq              = None
    self.training_range          = None
    self.included_exog           = False
    self.exog_type               = None
    self.exog_dtypes             = None
    self.exog_col_names          = None
    self.series_col_names        = None
    self.series_X_train          = None
    self.X_train_col_names       = 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.dropna_from_series      = False # Ignored in this forecaster

    if not isinstance(level, str):
        raise TypeError(
            f"`level` argument must be a str. Got {type(level)}."
        )

    if not isinstance(steps, int):
        raise TypeError(
            (f"`steps` argument must be an int greater than or equal to 1. "
             f"Got {type(steps)}.")
        )

    if steps < 1:
        raise ValueError(
            f"`steps` argument must be greater than or equal to 1. Got {steps}."
        )

    if not isinstance(n_jobs, int) and n_jobs != 'auto':
        raise TypeError(
            f"`n_jobs` must be an integer or `'auto'`. Got {type(n_jobs)}."
        )

    self.regressors_ = {step: clone(self.regressor) for step in range(1, steps + 1)}

    if isinstance(lags, dict):
        self.lags = {}
        for key in lags:
            if lags[key] is None:
                self.lags[key] = None
            else:
                self.lags[key] = initialize_lags(
                                     forecaster_name = type(self).__name__,
                                     lags            = lags[key]
                                 )
    else:
        self.lags = initialize_lags(
                        forecaster_name = type(self).__name__, 
                        lags            = lags
                    )

    self.lags_ = self.lags
    self.max_lag = (
        max(chain(*[v for v in self.lags.values() if v is not None]))
        if isinstance(self.lags, dict)
        else max(self.lags)
    )
    self.window_size = self.max_lag
    self.window_size_diff = self.max_lag

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

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

    self.in_sample_residuals = {step: None for step in range(1, steps + 1)}
    self.out_sample_residuals = None

    if n_jobs == 'auto':
        self.n_jobs = select_n_jobs_fit_forecaster(
                          forecaster_name = type(self).__name__,
                          regressor_name  = type(self.regressor).__name__,
                      )
    else:
        self.n_jobs = n_jobs if n_jobs > 0 else cpu_count()

_create_lags(y, lags, return_data='both')

Transforms a 1d array into a 2d array (X) and a 2d 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
lags	numpy ndarray	lags to create.	required
return_data	str	Specifies which data to return. Options are 'X', 'y', 'both'.	'both'

Returns:

Name	Type	Description
X_data	numpy ndarray	2d numpy ndarray with the lagged values (predictors). Will be None if return_data is 'y'. Shape: (samples - max(self.lags), len(self.lags))
y_data	numpy ndarray	2d numpy ndarray with the values of the time series related to each row of X_data for each step. Will be None if return_data is 'X'. Shape: (len(self.steps), samples - max(self.lags))

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def _create_lags(
    self, 
    y: np.ndarray,
    lags: np.ndarray,
    return_data: str = 'both'
) -> Tuple[Optional[np.ndarray], Optional[np.ndarray]]:
    """
    Transforms a 1d array into a 2d array (X) and a 2d 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.
    lags : numpy ndarray
        lags to create.
    return_data : str, default 'both'
        Specifies which data to return. Options are 'X', 'y', 'both'.

    Returns
    -------
    X_data : numpy ndarray
        2d numpy ndarray with the lagged values (predictors). Will be None if 
        `return_data` is 'y'. Shape: (samples - max(self.lags), len(self.lags))
    y_data : numpy ndarray
        2d numpy ndarray with the values of the time series related to each 
        row of `X_data` for each step. Will be None if `return_data` is 
        'X'. Shape: (len(self.steps), samples - max(self.lags))

    """

    n_splits = len(y) - self.max_lag - (self.steps - 1) # rows of y_data
    if n_splits <= 0:
        raise ValueError(
            (f"The maximum lag ({self.max_lag}) must be less than the length "
             f"of the series minus the number of steps ({len(y)-(self.steps-1)}).")
        )

    if return_data == 'y':
        X_data = None
    else:
        X_data = np.full(shape=(n_splits, len(lags)), fill_value=np.nan, dtype=float)
        for i, lag in enumerate(lags):
            X_data[:, i] = y[self.max_lag - lag : -(lag + self.steps - 1)] 

    if return_data == 'X':
        y_data = None
    else:       
        y_data = np.full(shape=(self.steps, n_splits), fill_value=np.nan, dtype=float)
        for step in range(self.steps):
            y_data[step, ] = y[self.max_lag + step : self.max_lag + step + n_splits]

    return X_data, y_data

_create_train_X_y(series, exog=None)

Create training matrices from multiple time series and exogenous variables. The resulting matrices contain the target variable and predictors needed to train all the regressors (one per step).

Parameters:

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

Returns:

Name	Type	Description
X_train	pandas DataFrame	Training values (predictors) for each step. Note that the index corresponds to that of the last step. It is updated for the corresponding step in the filter_train_X_y_for_step method. Shape: (len(series) - self.max_lag, len(self.lags)len(series.columns) + exog.shape[1]steps)
y_train	dict	Values (target) of the time series related to each row of X_train for each step of the form {step: y_step_[i]}. Shape of each series: (len(y) - self.max_lag, )
series_col_names	list	Names of the series (levels) provided by the user during training.
series_X_train	list	Names of the series added to X_train when creating the training matrices with _create_train_X_y method. It is a subset of series_col_names.
exog_col_names	list	Names of the exogenous variables included in the training matrices.

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def _create_train_X_y(
    self,
    series: pd.DataFrame,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> Tuple[pd.DataFrame, dict, list, list, list]:
    """
    Create training matrices from multiple time series and exogenous
    variables. The resulting matrices contain the target variable and predictors
    needed to train all the regressors (one per step).

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

    Returns
    -------
    X_train : pandas DataFrame
        Training values (predictors) for each step. Note that the index 
        corresponds to that of the last step. It is updated for the corresponding 
        step in the filter_train_X_y_for_step method.
        Shape: (len(series) - self.max_lag, len(self.lags)*len(series.columns) + exog.shape[1]*steps)
    y_train : dict
        Values (target) of the time series related to each row of `X_train` 
        for each step of the form {step: y_step_[i]}.
        Shape of each series: (len(y) - self.max_lag, )
    series_col_names : list
        Names of the series (levels) provided by the user during training.
    series_X_train : list
        Names of the series added to `X_train` when creating the training
        matrices with `_create_train_X_y` method. It is a subset of 
        `series_col_names`.
    exog_col_names : list
        Names of the exogenous variables included in the training matrices.

    """

    if not isinstance(series, pd.DataFrame):
        raise TypeError(
            f"`series` must be a pandas DataFrame. Got {type(series)}."
        )

    series_col_names = list(series.columns)

    if self.level not in series_col_names:
        raise ValueError(
            (f"One of the `series` columns must be named as the `level` of the forecaster.\n"
             f"  Forecaster `level` : {self.level}.\n"
             f"  `series` columns   : {series_col_names}.")
        )

    if isinstance(self.lags, dict):
        self.lags_ = self.lags
        lags_keys = list(self.lags_.keys())
        if lags_keys != series_col_names:
            raise ValueError(
                (f"When `lags` parameter is a `dict`, its keys must be the "
                 f"same as `series` column names.\n"
                 f"  Lags keys        : {lags_keys}.\n"
                 f"  `series` columns : {series_col_names}.")
            )
    else:
        self.lags_ = {serie: self.lags for serie in series_col_names}

    # If col is not level and has lags, create 'X' if no lags don't include
    # If col is level, create 'both' (`X` and `y`)
    cols_to_create_lags = {
        col: ('both' if col == self.level else 'X')
        for col in series_col_names
        if col == self.level or self.lags_.get(col) is not None
    }

    # Adjust 'level' in case self.lags_[level] is None
    if self.lags_.get(self.level) is None:
        cols_to_create_lags[self.level] = 'y'

    # Update series_col_names with the columns that will be used during training
    series_col_names = list(cols_to_create_lags.keys())
    # series_X_train include series that will be added to X_train
    series_X_train = [col for col in series_col_names 
                      if cols_to_create_lags[col] in ['X', 'both']]

    if len(series) < self.max_lag + self.steps:
        raise ValueError(
            (f"Minimum length of `series` for training this forecaster is "
             f"{self.max_lag + self.steps}. Got {len(series)}. Reduce the "
             f"number of predicted steps, {self.steps}, or the maximum "
             f"lag, {self.max_lag}, if no more data is available.")
        )

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

    exog_col_names = None
    if exog is not None:
        if not isinstance(exog, (pd.Series, pd.DataFrame)):
            raise TypeError(
                f"`exog` must be a pandas Series or DataFrame. Got {type(exog)}."
            )

        exog_col_names = \
            exog.columns.to_list() if isinstance(exog, pd.DataFrame) else [exog.name]
        if len(set(exog_col_names) - set(series_col_names)) != len(exog_col_names):
            raise ValueError(
                (f"`exog` cannot contain a column named the same as one of "
                 f"the series (column names of series).\n"
                 f"  `series` columns : {series_col_names}.\n"
                 f"  `exog`   columns : {exog_col_names}.")
            )

        if len(exog) != len(series):
            raise ValueError(
                (f"`exog` must have same number of samples as `series`. "
                 f"length `exog`: ({len(exog)}), length `series`: ({len(series)})")
            )
        check_exog(exog=exog, allow_nan=True)
        # Need here for filter_train_X_y_for_step to work without fitting
        self.included_exog = True 
        if isinstance(exog, pd.Series):
            exog = transform_series(
                       series            = exog,
                       transformer       = self.transformer_exog,
                       fit               = True,
                       inverse_transform = False
                   )
        else:
            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = True,
                       inverse_transform = False
                   )

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

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

    X_train_list = []
    X_train_col_names = []
    for col, return_data in cols_to_create_lags.items():

        y = series[col]
        check_y(y=y, series_id=f"Column '{col}'")
        y = transform_series(
                series            = y,
                transformer       = self.transformer_series_[col],
                fit               = True,
                inverse_transform = False
            )
        y_values, y_index = preprocess_y(y=y)

        X_train_values, y_train_values = self._create_lags(
                                             y           = y_values,
                                             lags        = self.lags_[col],
                                             return_data = return_data
                                         )

        if X_train_values is not None:
            X_train_list.append(X_train_values)
            X_train_col_names.extend(
                [f"{col}_lag_{lag}" for lag in self.lags_[col]]
            )
        if col == self.level:
            y_train = y_train_values


    X_train = pd.DataFrame(
                  data    = np.hstack(X_train_list),
                  columns = X_train_col_names,
                  index   = y_index[self.max_lag + (self.steps -1): ]
              )

    if exog is not None:
        # Transform exog to match direct format
        # The first `self.max_lag` positions have to be removed from X_exog
        # since they are not in X_lags.
        exog_to_train = exog_to_direct(
                            exog  = exog,
                            steps = self.steps
                        ).iloc[-X_train.shape[0]:, :]
        exog_to_train.index = exog_index[-X_train.shape[0]:]
        X_train = pd.concat((X_train, exog_to_train), axis=1)

    # Need here for filter_train_X_y_for_step to work without fitting
    self.X_train_col_names = X_train.columns.to_list()

    y_train = {
        step: pd.Series(
                  data  = y_train[step-1], 
                  index = y_index[self.max_lag + step-1:][:len(y_train[0])],
                  name  = f"{self.level}_step_{step}"
              )
        for step in range(1, self.steps + 1)
    }

    return X_train, y_train, series_col_names, series_X_train, exog_col_names

create_train_X_y(series, exog=None)

Create training matrices from multiple time series and exogenous variables. The resulting matrices contain the target variable and predictors needed to train all the regressors (one per step).

Parameters:

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

Returns:

Name	Type	Description
X_train	pandas DataFrame	Training values (predictors) for each step. Note that the index corresponds to that of the last step. It is updated for the corresponding step in the filter_train_X_y_for_step method. Shape: (len(series) - self.max_lag, len(self.lags)len(series.columns) + exog.shape[1]steps)
y_train	dict	Values (target) of the time series related to each row of X_train for each step of the form {step: y_step_[i]}. Shape of each series: (len(y) - self.max_lag, )

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def create_train_X_y(
    self,
    series: pd.DataFrame,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> Tuple[pd.DataFrame, dict, list, list, list]:
    """
    Create training matrices from multiple time series and exogenous
    variables. The resulting matrices contain the target variable and predictors
    needed to train all the regressors (one per step).

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

    Returns
    -------
    X_train : pandas DataFrame
        Training values (predictors) for each step. Note that the index 
        corresponds to that of the last step. It is updated for the corresponding 
        step in the filter_train_X_y_for_step method.
        Shape: (len(series) - self.max_lag, len(self.lags)*len(series.columns) + exog.shape[1]*steps)
    y_train : dict
        Values (target) of the time series related to each row of `X_train` 
        for each step of the form {step: y_step_[i]}.
        Shape of each series: (len(y) - self.max_lag, )

    """

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

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

    return X_train, y_train

filter_train_X_y_for_step(step, X_train, y_train, remove_suffix=False)

Select the columns needed to train a forecaster for a specific step.
The input matrices should be created using _create_train_X_y method. This method updates the index of X_train to the corresponding one according to y_train. If remove_suffix=True the suffix "_step_i" will be removed from the column names.

Parameters:

Name	Type	Description	Default
step	int	step for which columns must be selected selected. Starts at 1.	required
X_train	pandas DataFrame	Dataframe created with the _create_train_X_y method, first return.	required
y_train	dict	Dict created with the _create_train_X_y method, second return.	required
remove_suffix	bool	If True, suffix "_step_i" is removed from the column names.	`False`

Returns:

Name	Type	Description
X_train_step	pandas DataFrame	Training values (predictors) for the selected step.
y_train_step	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\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def filter_train_X_y_for_step(
    self,
    step: int,
    X_train: pd.DataFrame,
    y_train: dict,
    remove_suffix: bool=False
) -> Tuple[pd.DataFrame, pd.Series]:
    """
    Select the columns needed to train a forecaster for a specific step.  
    The input matrices should be created using `_create_train_X_y` method. 
    This method updates the index of `X_train` to the corresponding one 
    according to `y_train`. If `remove_suffix=True` the suffix "_step_i" 
    will be removed from the column names. 

    Parameters
    ----------
    step : int
        step for which columns must be selected selected. Starts at 1.
    X_train : pandas DataFrame
        Dataframe created with the `_create_train_X_y` method, first return.
    y_train : dict
        Dict created with the `_create_train_X_y` method, second return.
    remove_suffix : bool, default `False`
        If True, suffix "_step_i" is removed from the column names.

    Returns
    -------
    X_train_step : pandas DataFrame
        Training values (predictors) for the selected step.
    y_train_step : pandas Series
        Values (target) of the time series related to each row of `X_train`.
        Shape: (len(y) - self.max_lag)

    """

    if (step < 1) or (step > self.steps):
        raise ValueError(
            (f"Invalid value `step`. For this forecaster, minimum value is 1 "
             f"and the maximum step is {self.steps}.")
        )

    y_train_step = y_train[step]

    # Matrix X_train starts at index 0.
    if not self.included_exog:
        X_train_step = X_train
    else:
        len_columns_lags = len(list(
            chain(*[v for v in self.lags_.values() if v is not None])
        ))
        idx_columns_lags = np.arange(len_columns_lags)
        n_exog = (len(self.X_train_col_names) - len_columns_lags) / self.steps
        idx_columns_exog = (
            np.arange((step-1)*n_exog, (step)*n_exog) + idx_columns_lags[-1] + 1 
        )
        idx_columns = np.hstack((idx_columns_lags, idx_columns_exog))
        X_train_step = X_train.iloc[:, idx_columns]

    X_train_step.index = y_train_step.index

    if remove_suffix:
        X_train_step.columns = [col.replace(f"_step_{step}", "")
                                for col in X_train_step.columns]
        y_train_step.name = y_train_step.name.replace(f"_step_{step}", "")

    return X_train_step, y_train_step

create_sample_weights(X_train)

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

Parameters:

Name	Type	Description	Default
X_train	pandas DataFrame	Dataframe created with _create_train_X_y and filter_train_X_y_for_step` methods, first return.	required

Returns:

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

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

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

    Parameters
    ----------
    X_train : pandas DataFrame
        Dataframe created with `_create_train_X_y` and filter_train_X_y_for_step`
        methods, first return.

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

    """

    sample_weight = None

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

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

    return sample_weight

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

Training Forecaster.

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

Parameters:

Name	Type	Description	Default
series	pandas DataFrame	Training time series.	required
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s. Must have the same number of observations as series and their indexes must be aligned so that series[i] is regressed on exog[i].	`None`
store_last_window	bool	Whether or not to store the last window of training data.	`True`
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting.	`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

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

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

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

    Parameters
    ----------
    series : pandas DataFrame
        Training time series.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `series` and their indexes must be aligned so
        that series[i] is regressed on exog[i].
    store_last_window : bool, default `True`
        Whether or not to store the last window of training data.
    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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    # Reset values in case the forecaster has already been fitted.
    self.index_type          = None
    self.index_freq          = None
    self.series_col_names    = None
    self.series_X_train      = None
    self.X_train_col_names   = None
    self.last_window         = None
    self.included_exog       = False
    self.exog_type           = None
    self.exog_dtypes         = None
    self.exog_col_names      = None
    self.in_sample_residuals = {step: None for step in range(1, self.steps + 1)}
    self.fitted              = False
    self.training_range      = None

    X_train, y_train, series_col_names, series_X_train, exog_col_names = (
        self._create_train_X_y(series=series, exog=exog)
    )

    def fit_forecaster(regressor, X_train, y_train, step, store_in_sample_residuals):
        """
        Auxiliary function to fit each of the forecaster's regressors in parallel.

        Parameters
        ----------
        regressor : object
            Regressor to be fitted.
        X_train : pandas DataFrame
            Dataframe created with the `_create_train_X_y` method, first return.
        y_train : dict
            Dict created with the `_create_train_X_y` method, second return.
        step : int
            Step of the forecaster to be fitted.
        store_in_sample_residuals : bool
            If `True`, in-sample residuals will be stored in the forecaster object
            after fitting.

        Returns
        -------
        Tuple with the step, fitted regressor and in-sample residuals.

        """

        X_train_step, y_train_step = self.filter_train_X_y_for_step(
                                         step          = step,
                                         X_train       = X_train,
                                         y_train       = y_train,
                                         remove_suffix = True
                                     )
        sample_weight = self.create_sample_weights(X_train=X_train_step)
        if sample_weight is not None:
            regressor.fit(
                X             = X_train_step,
                y             = y_train_step,
                sample_weight = sample_weight,
                **self.fit_kwargs
            )
        else:
            regressor.fit(
                X = X_train_step,
                y = y_train_step,
                **self.fit_kwargs
            )

        # This is done to save time during fit in functions such as backtesting()
        if store_in_sample_residuals:
            residuals = (
                (y_train_step - regressor.predict(X_train_step))
            ).to_numpy()

            if len(residuals) > 1000:
                # Only up to 1000 residuals are stored
                    rng = np.random.default_rng(seed=123)
                    residuals = rng.choice(
                                    a       = residuals, 
                                    size    = 1000, 
                                    replace = False
                                )
        else:
            residuals = None

        return step, regressor, residuals

    results_fit = (
        Parallel(n_jobs=self.n_jobs)
        (delayed(fit_forecaster)
        (
            regressor                 = copy(self.regressor),
            X_train                   = X_train,
            y_train                   = y_train,
            step                      = step,
            store_in_sample_residuals = store_in_sample_residuals
        )
        for step in range(1, self.steps + 1))
    )

    self.regressors_ = {step: regressor 
                        for step, regressor, _ in results_fit}

    if store_in_sample_residuals:
        self.in_sample_residuals = {step: residuals 
                                    for step, _, residuals in results_fit}

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

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

    if store_last_window:            
        self.last_window = series.iloc[-self.max_lag:, ][self.series_X_train].copy()

    set_skforecast_warnings(suppress_warnings, action='default')

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

Predict n steps ahead

Parameters:

Name	Type	Description	Default
steps	(int, list, None)	Predict n steps. The value of steps must be less than or equal to the value of steps defined when initializing the forecaster. Starts at 1. If int: Only steps within the range of 1 to int are predicted. If list: List of ints. Only the steps contained in the list are predicted. If None: As many steps are predicted as were defined at initialization.	`None`
last_window	pandas DataFrame	Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If last_window = None, the values stored in self.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	`None`
suppress_warnings	bool	If True, skforecast warnings will be suppressed during the prediction process. See skforecast.exceptions.warn_skforecast_categories for more information.	`False`
levels	Ignored	Not used, present here for API consistency by convention.	None

Returns:

Name	Type	Description
predictions	pandas DataFrame	Predicted values.

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def predict(
    self,
    steps: Optional[Union[int, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    suppress_warnings: bool=False,
    levels: Any=None
) -> pd.DataFrame:
    """
    Predict n steps ahead

    Parameters
    ----------
    steps : int, list, None, default `None`
        Predict n steps. The value of `steps` must be less than or equal to the 
        value of steps defined when initializing the forecaster. Starts at 1.

        - If `int`: Only steps within the range of 1 to int are predicted.
        - If `list`: List of ints. Only the steps contained in the list 
        are predicted.
        - If `None`: As many steps are predicted as were defined at 
        initialization.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in `self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s.
    suppress_warnings : bool, default `False`
        If `True`, skforecast warnings will be suppressed during the prediction 
        process. See skforecast.exceptions.warn_skforecast_categories for more
        information.
    levels : Ignored
        Not used, present here for API consistency by convention.

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    if isinstance(steps, int):
        steps = list(np.arange(steps) + 1)
    elif steps is None:
        steps = list(np.arange(self.steps) + 1)
    elif isinstance(steps, list):
        steps = list(np.array(steps))

    for step in steps:
        if not isinstance(step, (int, np.int64, np.int32)):
            raise TypeError(
                (f"`steps` argument must be an int, a list of ints or `None`. "
                 f"Got {type(steps)}.")
            )

    if last_window is None:
        last_window = self.last_window

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

    last_window = last_window.iloc[-self.window_size:, ][self.series_X_train].copy()

    if exog is not None:
        if isinstance(exog, pd.DataFrame):
            exog = transform_dataframe(
                       df                = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        else:
            exog = transform_series(
                       series            = exog,
                       transformer       = self.transformer_exog,
                       fit               = False,
                       inverse_transform = False
                   )
        check_exog_dtypes(exog=exog)
        exog_values = exog_to_direct_numpy(
                          exog  = exog.to_numpy()[:max(steps)],
                          steps = max(steps)
                      )[0]
    else:
        exog_values = None

    X_lags = np.array([[]], dtype=float)

    for serie in self.series_X_train:

        last_window_serie = transform_series(
                                series            = last_window[serie],
                                transformer       = self.transformer_series_[serie],
                                fit               = False,
                                inverse_transform = False
                            )

        last_window_values, last_window_index = preprocess_last_window(
                                                    last_window = last_window_serie
                                                )

        X_lags = np.hstack(
                    [X_lags, last_window_values[-self.lags_[serie]].reshape(1, -1)]
                 )

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

    if exog is None:
        Xs = [X_lags] * len(steps)
    else:
        n_exog = exog.shape[1] if isinstance(exog, pd.DataFrame) else 1
        Xs = [
            np.hstack(
                [X_lags, exog_values[(step-1)*n_exog:(step)*n_exog].reshape(1, -1)]
            )
            for step in steps
        ]

    regressors = [self.regressors_[step] for step in steps]
    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")
        predictions = [
            regressor.predict(X)[0] for regressor, X in zip(regressors, Xs)
        ]

    idx = expand_index(index=last_window_index, steps=max(steps))
    predictions = pd.DataFrame(
                      data    = predictions,
                      columns = [self.level],
                      index   = idx[np.array(steps)-1]
                  )

    predictions = transform_dataframe(
                      df                = predictions,
                      transformer       = self.transformer_series_[self.level],
                      fit               = False,
                      inverse_transform = True
                  )

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

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

Generate multiple forecasting predictions using a bootstrapping process. By sampling from a collection of past observed errors (the residuals), each iteration of bootstrapping generates a different set of predictions. See the Notes section for more information.

Parameters:

Name	Type	Description	Default
steps	(int, list, None)	Predict n steps. The value of steps must be less than or equal to the value of steps defined when initializing the forecaster. Starts at 1. If int: Only steps within the range of 1 to int are predicted. If list: List of ints. Only the steps contained in the list are predicted. If None: As many steps are predicted as were defined at initialization.	`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 inself.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	`None`
n_boot	int	Number of bootstrapping iterations used to estimate 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`
levels	Ignored	Not used, present here for API consistency by convention.	None

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

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

    Parameters
    ----------
    steps : int, list, None, default `None`
        Predict n steps. The value of `steps` must be less than or equal to the 
        value of steps defined when initializing the forecaster. Starts at 1.

        - If `int`: Only steps within the range of 1 to int are predicted.
        - If `list`: List of ints. Only the steps contained in the list 
        are predicted.
        - If `None`: As many steps are predicted as were defined at 
        initialization.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s.     
    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.
    levels : Ignored
        Not used, present here for API consistency by convention.

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

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    if self.fitted:
        if isinstance(steps, int):
            steps = list(np.arange(steps) + 1)
        elif steps is None:
            steps = list(np.arange(self.steps) + 1)
        elif isinstance(steps, list):
            steps = list(np.array(steps))

        if in_sample_residuals:
            if not set(steps).issubset(set(self.in_sample_residuals.keys())):
                raise ValueError(
                    (f"Not `forecaster.in_sample_residuals` for steps: "
                     f"{set(steps) - set(self.in_sample_residuals.keys())}.")
                )
            residuals = 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(steps).issubset(set(self.out_sample_residuals.keys())):
                    raise ValueError(
                        (f"Not `forecaster.out_sample_residuals` for steps: "
                         f"{set(steps) - set(self.out_sample_residuals.keys())}. "
                         f"Use method `set_out_sample_residuals()`.")
                    )
            residuals = self.out_sample_residuals

        check_residuals = (
            'forecaster.in_sample_residuals' if in_sample_residuals
            else 'forecaster.out_sample_residuals'
        )
        for step in steps:
            if residuals[step] is None:
                raise ValueError(
                    (f"forecaster residuals for step {step} are `None`. "
                     f"Check {check_residuals}.")
                )
            elif (any(element is None for element in residuals[step]) or
                  np.any(np.isnan(residuals[step]))):
                raise ValueError(
                    (f"forecaster residuals for step {step} contains `None` "
                     f"or `NaNs` values. Check {check_residuals}.")
                )

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

    # Predictions must be in the transformed scale before adding residuals
    predictions = transform_dataframe(
                      df                = predictions,
                      transformer       = self.transformer_series_[self.level],
                      fit               = False,
                      inverse_transform = False
                  )
    boot_predictions = pd.concat([predictions] * n_boot, axis=1)
    boot_predictions.columns= [f"pred_boot_{i}" for i in range(n_boot)]

    for i, step in enumerate(steps):
        rng = np.random.default_rng(seed=random_state)
        sample_residuals = rng.choice(
                               a       = residuals[step],
                               size    = n_boot,
                               replace = True
                           )
        boot_predictions.iloc[i, :] = boot_predictions.iloc[i, :] + sample_residuals

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return boot_predictions

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

Bootstrapping based predicted intervals. Both predictions and intervals are returned.

Parameters:

Name	Type	Description	Default
steps	(int, list, None)	Predict n steps. The value of steps must be less than or equal to the value of steps defined when initializing the forecaster. Starts at 1. If int: Only steps within the range of 1 to int are predicted. If list: List of ints. Only the steps contained in the list are predicted. If None: As many steps are predicted as were defined at initialization.	`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 inself.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	`None`
interval	list	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5].	`[5, 95]`
n_boot	int	Number of bootstrapping iterations used to estimate 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`
levels	Ignored	Not used, present here for API consistency by convention.	None

Returns:

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

Notes

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

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def predict_interval(
    self,
    steps: Optional[Union[int, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    interval: list=[5, 95],
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    suppress_warnings: bool=False,
    levels: Any=None
) -> pd.DataFrame:
    """
    Bootstrapping based predicted intervals.
    Both predictions and intervals are returned.

    Parameters
    ----------
    steps : int, list, None, default `None`
        Predict n steps. The value of `steps` must be less than or equal to the 
        value of steps defined when initializing the forecaster. Starts at 1.

        - If `int`: Only steps within the range of 1 to int are predicted.
        - If `list`: List of ints. Only the steps contained in the list 
        are predicted.
        - If `None`: As many steps are predicted as were defined at 
        initialization.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s.
    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 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.
    levels : Ignored
        Not used, present here for API consistency by convention.

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

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

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

    check_interval(interval=interval)

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

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

    interval = np.array(interval)/100
    predictions_interval = boot_predictions.quantile(q=interval, axis=1).transpose()
    predictions_interval.columns = [f'{self.level}_lower_bound', f'{self.level}_upper_bound']
    predictions = pd.concat((predictions, predictions_interval), axis=1)

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

predict_quantiles(steps=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, levels=None)

Bootstrapping based predicted quantiles.

Parameters:

Name	Type	Description	Default
steps	(int, list, None)	Predict n steps. The value of steps must be less than or equal to the value of steps defined when initializing the forecaster. Starts at 1. If int: Only steps within the range of 1 to int are predicted. If list: List of ints. Only the steps contained in the list are predicted. If None: As many steps are predicted as were defined at initialization.	`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 inself.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	`None`
quantiles	list	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`
levels	Ignored	Not used, present here for API consistency by convention.	None

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\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def predict_quantiles(
    self,
    steps: Optional[Union[int, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=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,
    levels: Any=None
) -> pd.DataFrame:
    """
    Bootstrapping based predicted quantiles.

    Parameters
    ----------
    steps : int, list, None, default `None`
        Predict n steps. The value of `steps` must be less than or equal to the 
        value of steps defined when initializing the forecaster. Starts at 1.

        - If `int`: Only steps within the range of 1 to int are predicted.
        - If `list`: List of ints. Only the steps contained in the list 
        are predicted.
        - If `None`: As many steps are predicted as were defined at 
        initialization.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s.
    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.
    levels : Ignored
        Not used, present here for API consistency by convention.

    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,
                           last_window         = last_window,
                           exog                = exog,
                           n_boot              = n_boot,
                           random_state        = random_state,
                           in_sample_residuals = in_sample_residuals
                       )

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

    set_skforecast_warnings(suppress_warnings, action='default')

    return predictions

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

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
distribution	Object	A distribution object from scipy.stats.	required
steps	(int, list, None)	Predict n steps. The value of steps must be less than or equal to the value of steps defined when initializing the forecaster. Starts at 1. If int: Only steps within the range of 1 to int are predicted. If list: List of ints. Only the steps contained in the list are predicted. If None: As many steps are predicted as were defined at initialization.	`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 inself.last_window are used to calculate the initial predictors, and the predictions start right after training data.	`None`
exog	pandas Series, pandas DataFrame	Exogenous variable/s included as predictor/s.	`None`
n_boot	int	Number of bootstrapping iterations used to estimate 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`
levels	Ignored	Not used, present here for API consistency by convention.	None

Returns:

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

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def predict_dist(
    self,
    distribution: object,
    steps: Optional[Union[int, list]]=None,
    last_window: Optional[pd.DataFrame]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    suppress_warnings: bool=False,
    levels: Any=None
) -> 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
    ----------
    distribution : Object
        A distribution object from scipy.stats.
    steps : int, list, None, default `None`
        Predict n steps. The value of `steps` must be less than or equal to the 
        value of steps defined when initializing the forecaster. Starts at 1.

        - If `int`: Only steps within the range of 1 to int are predicted.
        - If `list`: List of ints. Only the steps contained in the list 
        are predicted.
        - If `None`: As many steps are predicted as were defined at 
        initialization.
    last_window : pandas DataFrame, default `None`
        Series values used to create the predictors (lags) needed in the 
        first iteration of the prediction (t + 1).
        If `last_window = None`, the values stored in` self.last_window` are
        used to calculate the initial predictors, and the predictions start
        right after training data.
    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s.
    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.
    levels : Ignored
        Not used, present here for API consistency by convention.

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

    """

    set_skforecast_warnings(suppress_warnings, action='ignore')

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

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

    level_param_names = [f'{self.level}_{p}' for p in param_names]
    predictions = pd.DataFrame(
                      data    = param_values,
                      columns = level_param_names,
                      index   = boot_samples.index
                  )

    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. It is important to note that all models share the same configuration of parameters and hyperparameters.

Parameters:

Name	Type	Description	Default
params	dict	Parameters values.	required

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def set_params(
    self, 
    params: dict
) -> None:
    """
    Set new values to the parameters of the scikit learn model stored in the
    forecaster. It is important to note that all models share the same 
    configuration of parameters and hyperparameters.

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

    Returns
    -------
    None

    """

    self.regressor = clone(self.regressor)
    self.regressor.set_params(**params)
    self.regressors_ = {step: clone(self.regressor)
                        for step in range(1, self.steps + 1)}

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\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.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, dict	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. dict: create different lags for each series. {'series_column_name': lags}.	required

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def set_lags(
    self, 
    lags: Union[int, np.ndarray, list, dict]
) -> 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, dict
        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.
        - `dict`: create different lags for each series. 
        {'series_column_name': lags}.

    Returns
    -------
    None

    """

    if isinstance(lags, dict):
        self.lags = {}
        for key in lags:
            if isinstance(lags[key], type(None)):
                self.lags[key] = None
            else:
                self.lags[key] = initialize_lags(
                                     forecaster_name = type(self).__name__,
                                     lags            = lags[key]
                                 )
    else:
        self.lags = initialize_lags(
                        forecaster_name = type(self).__name__, 
                        lags            = lags
                    )

    self.lags_ = self.lags
    self.max_lag = (
        max(chain(*[v for v in self.lags.values() if v is not None]))
        if isinstance(self.lags, dict)
        else max(self.lags)
    )
    self.window_size = self.max_lag
    self.window_size_diff = self.max_lag

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

Returns:

Type	Description
None

Source code in skforecast\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.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 model in the
        form {step: residuals}. If len(residuals) > 1000, only a random 
        sample of 1000 values are stored.
    append : bool, default `True`
        If `True`, new residuals are added to the once already stored in the
        attribute `out_sample_residuals`. Once the limit of 1000 values is
        reached, no more values are appended. If False, `out_sample_residuals`
        is overwritten with the new residuals.
    transform : bool, default `True`
        If `True`, new residuals are transformed using self.transformer_y.
    random_state : int, default `123`
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    None

    """

    if not isinstance(residuals, 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 "
             "`{step: 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 = {step: None 
                                     for step in range(1, self.steps + 1)}

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

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

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

    if transform and self.transformer_series_[self.level] is not None:
        warnings.warn(
            (f"Residuals will be transformed using the same transformer used when "
             f"training the forecaster ({self.transformer_series_[self.level]}). Ensure "
             f"the new residuals are on the same scale as the original time series.")
        )
        for key, value in residuals.items():
            residuals[key] = transform_series(
                                 series            = pd.Series(value, name='residuals'),
                                 transformer       = self.transformer_series_[self.level],
                                 fit               = False,
                                 inverse_transform = False
                             ).to_numpy()

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

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

        self.out_sample_residuals[key] = value

get_feature_importances(step, sort_importance=True)

Return feature importance of the model stored in the forecaster for a specific step. Since a separate model is created for each forecast time step, it is necessary to select the model from which retrieve information. Only valid when regressor stores internally the feature importances in the attribute feature_importances_ or coef_. Otherwise, it returns
None.

Parameters:

Name	Type	Description	Default
step	int	Model from which retrieve information (a separate model is created for each forecast time step). First step is 1.	required
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\ForecasterAutoregMultiVariate\ForecasterAutoregMultiVariate.py

def get_feature_importances(
    self,
    step: int,
    sort_importance: bool=True
) -> pd.DataFrame:
    """
    Return feature importance of the model stored in the forecaster for a
    specific step. Since a separate model is created for each forecast time
    step, it is necessary to select the model from which retrieve information.
    Only valid when regressor stores internally the feature importances in
    the attribute `feature_importances_` or `coef_`. Otherwise, it returns  
    `None`.

    Parameters
    ----------
    step : int
        Model from which retrieve information (a separate model is created 
        for each forecast time step). First step is 1.
    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 isinstance(step, int):
        raise TypeError(
            f"`step` must be an integer. Got {type(step)}."
        )

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

    if (step < 1) or (step > self.steps):
        raise ValueError(
            (f"The step must have a value from 1 to the maximum number of steps "
             f"({self.steps}). Got {step}.")
        )

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

    len_columns_lags = len(list(
        chain(*[v for v in self.lags_.values() if v is not None])
    ))
    idx_columns_lags = np.arange(len_columns_lags)
    if self.included_exog:
        idx_columns_exog = np.flatnonzero(
                               [name.endswith(f"step_{step}")
                                for name in self.X_train_col_names]
                           )
    else:
        idx_columns_exog = np.array([], dtype=int)

    idx_columns = np.hstack((idx_columns_lags, idx_columns_exog))
    feature_names = [self.X_train_col_names[i].replace(f"_step_{step}", "") 
                     for i in idx_columns]

    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': feature_names,
                                  'importance': feature_importances
                              })
        if sort_importance:
            feature_importances = feature_importances.sort_values(
                                      by='importance', ascending=False
                                  )

    return feature_importances