model_selection_multiseries

backtesting_forecaster_multiseries(forecaster, series, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, refit=False, interval=None, n_boot=500, random_state=123, in_sample_residuals=True, verbose=False, show_progress=True)

Backtesting for multi-series and multivariate forecasters.

If refit is False, the model is trained only once using the initial_train_size first observations. If refit is True, the model is trained in each iteration increasing the training set. A copy of the original forecaster is created so it is not modified during the process.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forecaster model.	required
series	DataFrame	Training time series.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	Optional[int]	Number of samples in the initial train split. If None and forecaster is already trained, no initial train is done and all data is used to evaluate the model. However, the first len(forecaster.last_window) observations are needed to create the initial predictors, so no predictions are calculated for them. None is only allowed when refit is False.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	Time series to be predicted. If None all levels will be predicted. New in version 0.6.0	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
refit	bool	Whether to re-fit the forecaster in each iteration.	False
interval	Optional[list]	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. If None, no intervals are estimated. Only available for forecaster of type ForecasterAutoreg and ForecasterAutoregCustom.	None
n_boot	int	Number of bootstrapping iterations used to estimate prediction intervals.	500
random_state	int	Sets a seed to the random generator, so that boot intervals are always deterministic.	123
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create prediction intervals. If False, out_sample_residuals are used if they are already stored inside the forecaster.	True
verbose	bool	Print number of folds and index of training and validation sets used for backtesting.	False
show_progress	bool	Whether to show a progress bar. Defaults to True.	True

Returns:

Type	Description
Tuple[pandas.core.frame.DataFrame, pandas.core.frame.DataFrame]	Value(s) of the metric(s). Index are the levels and columns the metrics.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def backtesting_forecaster_multiseries(
    forecaster,
    series: pd.DataFrame,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: Optional[int],
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    refit: bool=False,
    interval: Optional[list]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    verbose: bool=False,
    show_progress: bool=True
) -> Tuple[pd.DataFrame, pd.DataFrame]:
    """
    Backtesting for multi-series and multivariate forecasters.

    If `refit` is False, the model is trained only once using the `initial_train_size`
    first observations. If `refit` is True, the model is trained in each iteration
    increasing the training set. A copy of the original forecaster is created so 
    it is not modified during the process.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forecaster model.

    series : pandas DataFrame
        Training time series.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int, default `None`
        Number of samples in the initial train split. If `None` and `forecaster` is already 
        trained, no initial train is done and all data is used to evaluate the model. However, 
        the first `len(forecaster.last_window)` observations are needed to create the 
        initial predictors, so no predictions are calculated for them.

        `None` is only allowed when `refit` is `False`.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels will be predicted.
        **New in version 0.6.0**

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration.

    interval : list, default `None`
        Confidence of the prediction interval estimated. Sequence of percentiles
        to compute, which must be between 0 and 100 inclusive. If `None`, no
        intervals are estimated. Only available for forecaster of type ForecasterAutoreg
        and ForecasterAutoregCustom.

    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate prediction
        intervals.

    random_state : int, default `123`
        Sets a seed to the random generator, so that boot intervals are always 
        deterministic.

    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create prediction intervals.  If `False`, out_sample_residuals
        are used if they are already stored inside the forecaster.

    verbose : bool, default `False`
        Print number of folds and index of training and validation sets used 
        for backtesting.

    show_progress: bool, default `True`
        Whether to show a progress bar. Defaults to True.

    Returns 
    -------
    metrics_levels : pandas DataFrame
        Value(s) of the metric(s). Index are the levels and columns the metrics.

    backtest_predictions : pandas DataFrame
        Value of predictions and their estimated interval if `interval` is not `None`.
        If there is more than one level, this structure will be repeated for each of them.
            column pred = predictions.
            column lower_bound = lower bound of the interval.
            column upper_bound = upper bound interval of the interval.

    """

    if type(forecaster).__name__ not in ['ForecasterAutoregMultiSeries', 
                                         'ForecasterAutoregMultiSeriesCustom', 
                                         'ForecasterAutoregMultiVariate']:
        raise TypeError(
            ("`forecaster` must be of type `ForecasterAutoregMultiSeries`, "
             "`ForecasterAutoregMultiSeriesCustom` or `ForecasterAutoregMultiVariate`, "
             "for all other types of forecasters use the functions available in "
             f"the `model_selection` module. Got {type(forecaster).__name__}")
        )

    check_backtesting_input(
        forecaster            = forecaster,
        steps                 = steps,
        metric                = metric,
        series                = series,
        initial_train_size    = initial_train_size,
        fixed_train_size      = fixed_train_size,
        gap                   = gap,
        allow_incomplete_fold = allow_incomplete_fold,
        refit                 = refit,
        interval              = interval,
        n_boot                = n_boot,
        random_state          = random_state,
        in_sample_residuals   = in_sample_residuals,
        verbose               = verbose,
        show_progress         = show_progress
    )

    if type(forecaster).__name__ in ['ForecasterAutoregMultiSeries', 
                                     'ForecasterAutoregMultiSeriesCustom'] \
        and levels is not None and not isinstance(levels, (str, list)):
        raise TypeError(
            ("`levels` must be a `list` of column names, a `str` of a column name "
             "or `None` when using a `ForecasterAutoregMultiSeries` or "
             "`ForecasterAutoregMultiSeriesCustom`. If the forecaster is of type "
             "`ForecasterAutoregMultiVariate`, this argument is ignored.")
        )

    if type(forecaster).__name__ == 'ForecasterAutoregMultiVariate' \
        and levels and levels != forecaster.level and levels != [forecaster.level]:
        warnings.warn(
            (f"`levels` argument have no use when the forecaster is of type "
             f"`ForecasterAutoregMultiVariate`. The level of this forecaster is "
             f"{forecaster.level}, to predict another level, change the `level` "
             f"argument when initializing the forecaster."),
             IgnoredArgumentWarning
        )

    if refit:
        metrics_levels, backtest_predictions = _backtesting_forecaster_multiseries_refit(
            forecaster            = forecaster,
            series                = series,
            steps                 = steps,
            levels                = levels,
            metric                = metric,
            initial_train_size    = initial_train_size,
            fixed_train_size      = fixed_train_size,
            gap                   = gap,
            allow_incomplete_fold = allow_incomplete_fold,
            exog                  = exog,
            interval              = interval,
            n_boot                = n_boot,
            random_state          = random_state,
            in_sample_residuals   = in_sample_residuals,
            verbose               = verbose,
            show_progress         = show_progress
        )
    else:
        metrics_levels, backtest_predictions = _backtesting_forecaster_multiseries_no_refit(
            forecaster            = forecaster,
            series                = series,
            steps                 = steps,
            levels                = levels,
            metric                = metric,
            initial_train_size    = initial_train_size,
            gap                   = gap,
            allow_incomplete_fold = allow_incomplete_fold,
            exog                  = exog,
            interval              = interval,
            n_boot                = n_boot,
            random_state          = random_state,
            in_sample_residuals   = in_sample_residuals,
            verbose               = verbose,
            show_progress         = show_progress
        )

    return metrics_levels, backtest_predictions

grid_search_forecaster_multiseries(forecaster, series, param_grid, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, lags_grid=None, refit=False, return_best=True, verbose=True)

Exhaustive search over specified parameter values for a Forecaster object.

Validation is done using multi-series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forcaster model.	required
series	DataFrame	Training time series.	required
param_grid	dict	Dictionary with parameters names (str) as keys and lists of parameter settings to try as values.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	int	Number of samples in the initial train split.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	level (str) or levels (list) at which the forecaster is optimized. If None, all levels are taken into account. The resulting metric will be the average of the optimization of all levels.	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
lags_grid	Optional[list]	Lists of lags to try. Only used if forecaster is an instance of ForecasterAutoregMultiSeries or ForecasterAutoregMultiVariate.	None
refit	bool	Whether to re-fit the forecaster in each iteration of backtesting.	False
return_best	bool	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool	Print number of folds used for cv or backtesting.	True

Returns:

Type	Description
DataFrame	Results for each combination of parameters. column levels = levels. column lags = predictions. column params = lower bound of the interval. column metric = metric(s) value(s) estimated for each combination of parameters. The resulting metric will be the average of the optimization of all levels. additional n columns with param = value.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def grid_search_forecaster_multiseries(
    forecaster,
    series: pd.DataFrame,
    param_grid: dict,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: int,
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    lags_grid: Optional[list]=None,
    refit: bool=False,
    return_best: bool=True,
    verbose: bool=True
) -> pd.DataFrame:
    """
    Exhaustive search over specified parameter values for a Forecaster object.
    Validation is done using multi-series backtesting.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forcaster model.

    series : pandas DataFrame
        Training time series.

    param_grid : dict
        Dictionary with parameters names (`str`) as keys and lists of parameter
        settings to try as values.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int 
        Number of samples in the initial train split.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        level (`str`) or levels (`list`) at which the forecaster is optimized. 
        If `None`, all levels are taken into account. The resulting metric will be
        the average of the optimization of all levels.

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    lags_grid : list of int, lists, np.narray or range, default `None`
        Lists of `lags` to try. Only used if forecaster is an instance of 
        `ForecasterAutoregMultiSeries` or `ForecasterAutoregMultiVariate`.

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration of backtesting.

    return_best : bool, default `True`
        Refit the `forecaster` using the best found parameters on the whole data.

    verbose : bool, default `True`
        Print number of folds used for cv or backtesting.

    Returns 
    -------
    results : pandas DataFrame
        Results for each combination of parameters.
            column levels = levels.
            column lags = predictions.
            column params = lower bound of the interval.
            column metric = metric(s) value(s) estimated for each combination of 
                            parameters. The resulting metric will be the average 
                            of the optimization of all levels.
            additional n columns with param = value.

    """

    param_grid = list(ParameterGrid(param_grid))

    results = _evaluate_grid_hyperparameters_multiseries(
                  forecaster            = forecaster,
                  series                = series,
                  param_grid            = param_grid,
                  steps                 = steps,
                  metric                = metric,
                  initial_train_size    = initial_train_size,
                  fixed_train_size      = fixed_train_size,
                  gap                   = gap,
                  allow_incomplete_fold = allow_incomplete_fold,
                  levels                = levels,
                  exog                  = exog,
                  lags_grid             = lags_grid,
                  refit                 = refit,
                  return_best           = return_best,
                  verbose               = verbose
              )

    return results

random_search_forecaster_multiseries(forecaster, series, param_distributions, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, lags_grid=None, refit=False, n_iter=10, random_state=123, return_best=True, verbose=True)

Random search over specified parameter values or distributions for a Forecaster

object. Validation is done using multi-series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forcaster model.	required
series	DataFrame	Training time series.	required
param_distributions	dict	Dictionary with parameters names (str) as keys and distributions or lists of parameters to try.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	int	Number of samples in the initial train split.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	level (str) or levels (list) at which the forecaster is optimized. If None, all levels are taken into account. The resulting metric will be the average of the optimization of all levels.	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
lags_grid	Optional[list]	Lists of lags to try. Only used if forecaster is an instance of ForecasterAutoregMultiSeries or ForecasterAutoregMultiVariate.	None
refit	bool	Whether to re-fit the forecaster in each iteration of backtesting.	False
n_iter	int	Number of parameter settings that are sampled per lags configuration. n_iter trades off runtime vs quality of the solution.	10
random_state	int	Sets a seed to the random sampling for reproducible output.	123
return_best	bool	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool	Print number of folds used for cv or backtesting.	True

Returns:

Type	Description
DataFrame	Results for each combination of parameters. column levels = levels. column lags = predictions. column params = lower bound of the interval. column metric = metric(s) value(s) estimated for each combination of parameters. The resulting metric will be the average of the optimization of all levels. additional n columns with param = value.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def random_search_forecaster_multiseries(
    forecaster,
    series: pd.DataFrame,
    param_distributions: dict,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: int,
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    lags_grid: Optional[list]=None,
    refit: bool=False,
    n_iter: int=10,
    random_state: int=123,
    return_best: bool=True,
    verbose: bool=True
) -> pd.DataFrame:
    """
    Random search over specified parameter values or distributions for a Forecaster 
    object. Validation is done using multi-series backtesting.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forcaster model.

    series : pandas DataFrame
        Training time series.

    param_distributions : dict
        Dictionary with parameters names (`str`) as keys and 
        distributions or lists of parameters to try.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int 
        Number of samples in the initial train split.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        level (`str`) or levels (`list`) at which the forecaster is optimized. 
        If `None`, all levels are taken into account. The resulting metric will be
        the average of the optimization of all levels.

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    lags_grid : list of int, lists, np.narray or range, default `None`
        Lists of `lags` to try. Only used if forecaster is an instance of 
        `ForecasterAutoregMultiSeries` or `ForecasterAutoregMultiVariate`.

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration of backtesting.

    n_iter : int, default `10`
        Number of parameter settings that are sampled per lags configuration. 
        n_iter trades off runtime vs quality of the solution.

    random_state : int, default `123`
        Sets a seed to the random sampling for reproducible output.

    return_best : bool, default `True`
        Refit the `forecaster` using the best found parameters on the whole data.

    verbose : bool, default `True`
        Print number of folds used for cv or backtesting.

    Returns 
    -------
    results : pandas DataFrame
        Results for each combination of parameters.
            column levels = levels.
            column lags = predictions.
            column params = lower bound of the interval.
            column metric = metric(s) value(s) estimated for each combination of 
                            parameters. The resulting metric will be the average 
                            of the optimization of all levels.
            additional n columns with param = value.

    """

    param_grid = list(ParameterSampler(param_distributions, n_iter=n_iter, 
                                       random_state=random_state))

    results = _evaluate_grid_hyperparameters_multiseries(
                  forecaster            = forecaster,
                  series                = series,
                  param_grid            = param_grid,
                  steps                 = steps,
                  metric                = metric,
                  initial_train_size    = initial_train_size,
                  fixed_train_size      = fixed_train_size,
                  gap                   = gap,
                  allow_incomplete_fold = allow_incomplete_fold,
                  levels                = levels,
                  exog                  = exog,
                  lags_grid             = lags_grid,
                  refit                 = refit,
                  return_best           = return_best,
                  verbose               = verbose
              )

    return results

backtesting_forecaster_multivariate(forecaster, series, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, refit=False, interval=None, n_boot=500, random_state=123, in_sample_residuals=True, verbose=False, show_progress=True)

This function is an alias of backtesting_forecaster_multiseries.

Backtesting for multi-series and multivariate forecasters.

If refit is False, the model is trained only once using the initial_train_size first observations. If refit is True, the model is trained in each iteration increasing the training set. A copy of the original forecaster is created so it is not modified during the process.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forecaster model.	required
series	DataFrame	Training time series.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	Optional[int]	Number of samples in the initial train split. If None and forecaster is already trained, no initial train is done and all data is used to evaluate the model. However, the first len(forecaster.last_window) observations are needed to create the initial predictors, so no predictions are calculated for them. None is only allowed when refit is False.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	Time series to be predicted. If None all levels will be predicted. New in version 0.6.0	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
refit	bool	Whether to re-fit the forecaster in each iteration.	False
interval	Optional[list]	Confidence of the prediction interval estimated. Sequence of percentiles to compute, which must be between 0 and 100 inclusive. If None, no intervals are estimated. Only available for forecaster of type ForecasterAutoreg and ForecasterAutoregCustom.	None
n_boot	int	Number of bootstrapping iterations used to estimate prediction intervals.	500
random_state	int	Sets a seed to the random generator, so that boot intervals are always deterministic.	123
in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create prediction intervals. If False, out_sample_residuals are used if they are already stored inside the forecaster.	True
verbose	bool	Print number of folds and index of training and validation sets used for backtesting.	False
show_progress	bool	Whether to show a progress bar. Defaults to True.	True

Returns:

Type	Description
Tuple[pandas.core.frame.DataFrame, pandas.core.frame.DataFrame]	Value(s) of the metric(s). Index are the levels and columns the metrics.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def backtesting_forecaster_multivariate(
    forecaster,
    series: pd.DataFrame,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: Optional[int],
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    refit: bool=False,
    interval: Optional[list]=None,
    n_boot: int=500,
    random_state: int=123,
    in_sample_residuals: bool=True,
    verbose: bool=False,
    show_progress: bool=True
) -> Tuple[pd.DataFrame, pd.DataFrame]:
    """
    This function is an alias of backtesting_forecaster_multiseries.

    Backtesting for multi-series and multivariate forecasters.

    If `refit` is False, the model is trained only once using the `initial_train_size`
    first observations. If `refit` is True, the model is trained in each iteration
    increasing the training set. A copy of the original forecaster is created so 
    it is not modified during the process.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forecaster model.

    series : pandas DataFrame
        Training time series.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int, default `None`
        Number of samples in the initial train split. If `None` and `forecaster` is already 
        trained, no initial train is done and all data is used to evaluate the model. However, 
        the first `len(forecaster.last_window)` observations are needed to create the 
        initial predictors, so no predictions are calculated for them.

        `None` is only allowed when `refit` is `False`.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        Time series to be predicted. If `None` all levels will be predicted.
        **New in version 0.6.0**

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration.

    interval : list, default `None`
        Confidence of the prediction interval estimated. Sequence of percentiles
        to compute, which must be between 0 and 100 inclusive. If `None`, no
        intervals are estimated. Only available for forecaster of type ForecasterAutoreg
        and ForecasterAutoregCustom.

    n_boot : int, default `500`
        Number of bootstrapping iterations used to estimate prediction
        intervals.

    random_state : int, default `123`
        Sets a seed to the random generator, so that boot intervals are always 
        deterministic.

    in_sample_residuals : bool, default `True`
        If `True`, residuals from the training data are used as proxy of
        prediction error to create prediction intervals.  If `False`, out_sample_residuals
        are used if they are already stored inside the forecaster.

    verbose : bool, default `False`
        Print number of folds and index of training and validation sets used for backtesting.

    show_progress: bool, default `True`
        Whether to show a progress bar. Defaults to True.

    Returns 
    -------
    metrics_levels : pandas DataFrame
        Value(s) of the metric(s). Index are the levels and columns the metrics.

    backtest_predictions : pandas DataFrame
        Value of predictions and their estimated interval if `interval` is not `None`.
        If there is more than one level, this structure will be repeated for each of them.
            column pred = predictions.
            column lower_bound = lower bound of the interval.
            column upper_bound = upper bound interval of the interval.

    """

    metrics_levels, backtest_predictions = backtesting_forecaster_multiseries(
        forecaster            = forecaster,
        series                = series,
        steps                 = steps,
        metric                = metric,
        initial_train_size    = initial_train_size,
        fixed_train_size      = fixed_train_size,
        gap                   = gap,
        allow_incomplete_fold = allow_incomplete_fold,
        levels                = levels,
        exog                  = exog,
        refit                 = refit,
        interval              = interval,
        n_boot                = n_boot,
        random_state          = random_state,
        in_sample_residuals   = in_sample_residuals,
        verbose               = verbose,
        show_progress         = show_progress

    )

    return metrics_levels, backtest_predictions

grid_search_forecaster_multivariate(forecaster, series, param_grid, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, lags_grid=None, refit=False, return_best=True, verbose=True)

This function is an alias of grid_search_forecaster_multiseries.

Exhaustive search over specified parameter values for a Forecaster object. Validation is done using multi-series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forcaster model.	required
series	DataFrame	Training time series.	required
param_grid	dict	Dictionary with parameters names (str) as keys and lists of parameter settings to try as values.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	int	Number of samples in the initial train split.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	level (str) or levels (list) at which the forecaster is optimized. If None, all levels are taken into account. The resulting metric will be the average of the optimization of all levels.	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
lags_grid	Optional[list]	Lists of lags to try. Only used if forecaster is an instance of ForecasterAutoregMultiSeries or ForecasterAutoregMultiVariate.	None
refit	bool	Whether to re-fit the forecaster in each iteration of backtesting.	False
return_best	bool	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool	Print number of folds used for cv or backtesting.	True

Returns:

Type	Description
DataFrame	Results for each combination of parameters. column levels = levels. column lags = predictions. column params = lower bound of the interval. column metric = metric(s) value(s) estimated for each combination of parameters. The resulting metric will be the average of the optimization of all levels. additional n columns with param = value.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def grid_search_forecaster_multivariate(
    forecaster,
    series: pd.DataFrame,
    param_grid: dict,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: int,
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    lags_grid: Optional[list]=None,
    refit: bool=False,
    return_best: bool=True,
    verbose: bool=True
) -> pd.DataFrame:
    """
    This function is an alias of grid_search_forecaster_multiseries.

    Exhaustive search over specified parameter values for a Forecaster object.
    Validation is done using multi-series backtesting.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forcaster model.

    series : pandas DataFrame
        Training time series.

    param_grid : dict
        Dictionary with parameters names (`str`) as keys and lists of parameter
        settings to try as values.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int 
        Number of samples in the initial train split.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        level (`str`) or levels (`list`) at which the forecaster is optimized. 
        If `None`, all levels are taken into account. The resulting metric will be
        the average of the optimization of all levels.

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    lags_grid : list of int, lists, np.narray or range, default `None`
        Lists of `lags` to try. Only used if forecaster is an instance of 
        `ForecasterAutoregMultiSeries` or `ForecasterAutoregMultiVariate`.

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration of backtesting.

    return_best : bool, default `True`
        Refit the `forecaster` using the best found parameters on the whole data.

    verbose : bool, default `True`
        Print number of folds used for cv or backtesting.

    Returns 
    -------
    results : pandas DataFrame
        Results for each combination of parameters.
            column levels = levels.
            column lags = predictions.
            column params = lower bound of the interval.
            column metric = metric(s) value(s) estimated for each combination of 
                            parameters. The resulting metric will be the average 
                            of the optimization of all levels.
            additional n columns with param = value.

    """

    results = grid_search_forecaster_multiseries(
        forecaster            = forecaster,
        series                = series,
        param_grid            = param_grid,
        steps                 = steps,
        metric                = metric,
        initial_train_size    = initial_train_size,
        fixed_train_size      = fixed_train_size,
        gap                   = gap,
        allow_incomplete_fold = allow_incomplete_fold,
        levels                = levels,
        exog                  = exog,
        lags_grid             = lags_grid,
        refit                 = refit,
        return_best           = return_best,
        verbose               = verbose
    )

    return results

random_search_forecaster_multivariate(forecaster, series, param_distributions, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, levels=None, exog=None, lags_grid=None, refit=False, n_iter=10, random_state=123, return_best=True, verbose=True)

This function is an alias of random_search_forecaster_multiseries.

Random search over specified parameter values or distributions for a Forecaster object. Validation is done using multi-series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate	Forcaster model.	required
series	DataFrame	Training time series.	required
param_distributions	dict	Dictionary with parameters names (str) as keys and distributions or lists of parameters to try.	required
steps	int	Number of steps to predict.	required
metric	Union[str, Callable, list]	Metric used to quantify the goodness of fit of the model. If string: {'mean_squared_error', 'mean_absolute_error', 'mean_absolute_percentage_error', 'mean_squared_log_error'} If Callable: Function with arguments y_true, y_pred that returns a float. If list: List containing multiple strings and/or Callables.	required
initial_train_size	int	Number of samples in the initial train split.	required
fixed_train_size	bool	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
levels	Union[str, list]	level (str) or levels (list) at which the forecaster is optimized. If None, all levels are taken into account. The resulting metric will be the average of the optimization of all levels.	None
exog	Union[pandas.core.series.Series, pandas.core.frame.DataFrame]	Exogenous variable/s included as predictor/s. Must have the same number of observations as y and should be aligned so that y[i] is regressed on exog[i].	None
lags_grid	Optional[list]	Lists of lags to try. Only used if forecaster is an instance of ForecasterAutoregMultiSeries or ForecasterAutoregMultiVariate.	None
refit	bool	Whether to re-fit the forecaster in each iteration of backtesting.	False
n_iter	int	Number of parameter settings that are sampled per lags configuration. n_iter trades off runtime vs quality of the solution.	10
random_state	int	Sets a seed to the random sampling for reproducible output.	123
return_best	bool	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool	Print number of folds used for cv or backtesting.	True

Returns:

Type	Description
DataFrame	Results for each combination of parameters. column levels = levels. column lags = predictions. column params = lower bound of the interval. column metric = metric(s) value(s) estimated for each combination of parameters. The resulting metric will be the average of the optimization of all levels. additional n columns with param = value.

Source code in skforecast/model_selection_multiseries/model_selection_multiseries.py

def random_search_forecaster_multivariate(
    forecaster,
    series: pd.DataFrame,
    param_distributions: dict,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: int,
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    levels: Optional[Union[str, list]]=None,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    lags_grid: Optional[list]=None,
    refit: bool=False,
    n_iter: int=10,
    random_state: int=123,
    return_best: bool=True,
    verbose: bool=True
) -> pd.DataFrame:
    """
    This function is an alias of random_search_forecaster_multiseries.

    Random search over specified parameter values or distributions for a Forecaster 
    object. Validation is done using multi-series backtesting.

    Parameters
    ----------
    forecaster : ForecasterAutoregMultiSeries, ForecasterAutoregMultiSeriesCustom, ForecasterAutoregMultiVariate
        Forcaster model.

    series : pandas DataFrame
        Training time series.

    param_distributions : dict
        Dictionary with parameters names (`str`) as keys and 
        distributions or lists of parameters to try.

    steps : int
        Number of steps to predict.

    metric : str, Callable, list
        Metric used to quantify the goodness of fit of the model.

        If string:
            {'mean_squared_error', 'mean_absolute_error',
             'mean_absolute_percentage_error', 'mean_squared_log_error'}

        If Callable:
            Function with arguments y_true, y_pred that returns a float.

        If list:
            List containing multiple strings and/or Callables.

    initial_train_size : int 
        Number of samples in the initial train split.

    fixed_train_size : bool, default `True`
        If True, train size doesn't increase but moves by `steps` in each iteration.

    gap : int, default `0`
        Number of samples to be excluded after the end of each training set and 
        before the test set.

    allow_incomplete_fold : bool, default `True`
        Last fold is allowed to have a smaller number of samples than the 
        `test_size`. If `False`, the last fold is excluded.

    levels : str, list, default `None`
        level (`str`) or levels (`list`) at which the forecaster is optimized. 
        If `None`, all levels are taken into account. The resulting metric will be
        the average of the optimization of all levels.

    exog : pandas Series, pandas DataFrame, default `None`
        Exogenous variable/s included as predictor/s. Must have the same
        number of observations as `y` and should be aligned so that y[i] is
        regressed on exog[i].

    lags_grid : list of int, lists, np.narray or range, default `None`
        Lists of `lags` to try. Only used if forecaster is an instance of 
        `ForecasterAutoregMultiSeries` or `ForecasterAutoregMultiVariate`.

    refit : bool, default `False`
        Whether to re-fit the forecaster in each iteration of backtesting.

    n_iter : int, default `10`
        Number of parameter settings that are sampled per lags configuration. 
        n_iter trades off runtime vs quality of the solution.

    random_state : int, default `123`
        Sets a seed to the random sampling for reproducible output.

    return_best : bool, default `True`
        Refit the `forecaster` using the best found parameters on the whole data.

    verbose : bool, default `True`
        Print number of folds used for cv or backtesting.

    Returns 
    -------
    results : pandas DataFrame
        Results for each combination of parameters.
            column levels = levels.
            column lags = predictions.
            column params = lower bound of the interval.
            column metric = metric(s) value(s) estimated for each combination of 
                            parameters. The resulting metric will be the average 
                            of the optimization of all levels.
            additional n columns with param = value.

    """

    results = random_search_forecaster_multiseries(
        forecaster            = forecaster,
        series                = series,
        param_distributions   = param_distributions,
        steps                 = steps,
        metric                = metric,
        initial_train_size    = initial_train_size,
        fixed_train_size      = fixed_train_size,
        gap                   = gap,
        allow_incomplete_fold = allow_incomplete_fold,
        levels                = levels,
        exog                  = exog,
        lags_grid             = lags_grid,
        refit                 = refit,
        n_iter                = n_iter,
        random_state          = random_state,
        return_best           = return_best,
        verbose               = verbose
    ) 

    return results