model_selection_sarimax

backtesting_sarimax(forecaster, y, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, exog=None, refit=False, alpha=None, interval=None, verbose=False, show_progress=True)

Backtesting of ForecasterSarimax.

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	ForecasterSarimax	Forecaster model.	required
y	pandas Series	Training time series.	required
steps	int	Number of steps to predict.	required
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.	required
initial_train_size	int	Number of samples in the initial train split. The backtest forecaster is trained using the first initial_train_size observations.	required
fixed_train_size	bool, default	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int, default	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool, default	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
exog	pandas Series, pandas DataFrame, default	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, default	Whether to re-fit the forecaster in each iteration.	False
alpha	float, default	The confidence intervals for the forecasts are (1 - alpha) %. If both, alpha and interval are provided, alpha will be used.	None
interval	list, default	Confidence of the prediction interval estimated. The values must be symmetric. 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]. If both, alpha and interval are provided, alpha will be used.	None
verbose	bool, default	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:

Name	Type	Description
metrics_value	float, list	Value(s) of the metric(s).
backtest_predictions	pandas DataFrame	Value of predictions and their estimated interval if interval is not None. column pred: predictions. column lower_bound: lower bound of the interval. column upper_bound: upper bound of the interval.

Source code in skforecast/model_selection_sarimax/model_selection_sarimax.py

def backtesting_sarimax(
    forecaster,
    y: pd.Series,
    steps: int,
    metric: Union[str, Callable, list],
    initial_train_size: int,
    fixed_train_size: bool=True,
    gap: int=0,
    allow_incomplete_fold: bool=True,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    refit: bool=False,
    alpha: Optional[float]=None,
    interval: Optional[list]=None,
    verbose: bool=False,
    show_progress: bool=True
) -> Tuple[Union[float, list], pd.DataFrame]:
    """
    Backtesting of ForecasterSarimax.

    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 : ForecasterSarimax
        Forecaster model.
    y : pandas Series
        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
        Number of samples in the initial train split. The backtest forecaster is
        trained using the first `initial_train_size` observations.
    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.
    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.
    alpha : float, default `0.05`
        The confidence intervals for the forecasts are (1 - alpha) %.
        If both, `alpha` and `interval` are provided, `alpha` will be used.
    interval : list, default `None`
        Confidence of the prediction interval estimated. The values must be
        symmetric. 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]`. If both, `alpha` and `interval` are 
        provided, `alpha` will be used.     
    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_value : float, list
        Value(s) of the metric(s).
    backtest_predictions : pandas DataFrame
        Value of predictions and their estimated interval if `interval` is not `None`.

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

    """

    if type(forecaster).__name__ not in ['ForecasterSarimax']:
        raise TypeError(
            ("`forecaster` must be of type `ForecasterSarimax`, for all other "
             "types of forecasters use the functions available in the other "
             "`model_selection` modules.")
        )

    check_backtesting_input(
        forecaster            = forecaster,
        steps                 = steps,
        metric                = metric,
        y                     = y,
        initial_train_size    = initial_train_size,
        fixed_train_size      = fixed_train_size,
        gap                   = gap,
        allow_incomplete_fold = allow_incomplete_fold,
        refit                 = refit,
        interval              = interval,
        alpha                 = alpha,
        verbose               = verbose,
        show_progress         = show_progress
    )

    if refit:
        metrics_values, backtest_predictions = _backtesting_sarimax_refit(
            forecaster            = forecaster,
            y                     = y,
            steps                 = steps,
            metric                = metric,
            initial_train_size    = initial_train_size,
            fixed_train_size      = fixed_train_size,
            gap                   = gap,
            allow_incomplete_fold = allow_incomplete_fold,
            exog                  = exog,
            alpha                 = alpha,
            interval              = interval,
            verbose               = verbose,
            show_progress         = show_progress
        )
    else:
        if gap != 0 or allow_incomplete_fold is not True:
            warnings.warn(
                ("When using `refit=False`, the `gap` and `allow_incomplete_fold`"
                 "arguments are ignored. Set `refit=True` to used them."), 
                 IgnoredArgumentWarning
            )

        metrics_values, backtest_predictions = _backtesting_sarimax_no_refit(
            forecaster            = forecaster,
            y                     = y,
            steps                 = steps,
            metric                = metric,
            initial_train_size    = initial_train_size,
            exog                  = exog,
            alpha                 = alpha,
            interval              = interval,
            verbose               = verbose,
            show_progress         = show_progress
        )

    return metrics_values, backtest_predictions

grid_search_sarimax(forecaster, y, param_grid, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, exog=None, refit=False, return_best=True, verbose=True)

Exhaustive search over specified parameter values for a ForecasterSarimax object. Validation is done using time series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterSarimax	Forcaster model.	required
y	pandas Series	Training time series values.	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	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. The backtest forecaster is trained using the first initial_train_size observations.	required
fixed_train_size	bool, default	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int, default	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool, default	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
exog	pandas Series, pandas DataFrame, default	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, default	Whether to re-fit the forecaster in each iteration of backtesting.	False
return_best	bool, default	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool, default	Print number of folds used for cv or backtesting.	True

Returns:

Name	Type	Description
results	pandas DataFrame	Results for each combination of parameters. column params: parameters configuration for each iteration. column metric: metric value estimated for each iteration. additional n columns with param = value.

Source code in skforecast/model_selection_sarimax/model_selection_sarimax.py

def grid_search_sarimax(
    forecaster,
    y: pd.Series,
    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,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
    refit: bool=False,
    return_best: bool=True,
    verbose: bool=True
) -> pd.DataFrame:
    """
    Exhaustive search over specified parameter values for a ForecasterSarimax object.
    Validation is done using time series backtesting.

    Parameters
    ----------
    forecaster : ForecasterSarimax
        Forcaster model.
    y : pandas Series
        Training time series values. 
    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. The backtest forecaster is
        trained using the first `initial_train_size` observations.
    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.
    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 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 params: parameters configuration for each iteration.
            - column metric: metric value estimated for each iteration.
            - additional n columns with param = value.

    """

    param_grid = list(ParameterGrid(param_grid))

    results = _evaluate_grid_hyperparameters_sarimax(
        forecaster            = forecaster,
        y                     = y,
        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,
        exog                  = exog,
        refit                 = refit,
        return_best           = return_best,
        verbose               = verbose
    )

    return results

random_search_sarimax(forecaster, y, param_distributions, steps, metric, initial_train_size, fixed_train_size=True, gap=0, allow_incomplete_fold=True, exog=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 time series backtesting.

Parameters:

Name	Type	Description	Default
forecaster	ForecasterSarimax	Forcaster model.	required
y	pandas Series	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	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. The backtest forecaster is trained using the first initial_train_size observations.	required
fixed_train_size	bool, default	If True, train size doesn't increase but moves by steps in each iteration.	True
gap	int, default	Number of samples to be excluded after the end of each training set and before the test set.	0
allow_incomplete_fold	bool, default	Last fold is allowed to have a smaller number of samples than the test_size. If False, the last fold is excluded.	True
exog	pandas Series, pandas DataFrame, default	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, default	Whether to re-fit the forecaster in each iteration of backtesting.	False
n_iter	int, default	Number of parameter settings that are sampled. n_iter trades off runtime vs quality of the solution.	10
random_state	int, default	Sets a seed to the random sampling for reproducible output.	123
return_best	bool, default	Refit the forecaster using the best found parameters on the whole data.	True
verbose	bool, default	Print number of folds used for cv or backtesting.	True

Returns:

Name	Type	Description
results	pandas DataFrame	Results for each combination of parameters. column params: parameters configuration for each iteration. column metric: metric value estimated for each iteration. additional n columns with param = value.

Source code in skforecast/model_selection_sarimax/model_selection_sarimax.py

def random_search_sarimax(
    forecaster,
    y: pd.Series,
    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,
    exog: Optional[Union[pd.Series, pd.DataFrame]]=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 time series backtesting.

    Parameters
    ----------
    forecaster : ForecasterSarimax
        Forcaster model.
    y : pandas Series
        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. The backtest forecaster is
        trained using the first `initial_train_size` observations.
    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.
    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 of backtesting.
    n_iter : int, default `10`
        Number of parameter settings that are sampled. 
        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 params: parameters configuration for each iteration.
            - column metric: metric value estimated for each iteration.
            - additional n columns with param = value.

    """

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

    results = _evaluate_grid_hyperparameters_sarimax(
        forecaster            = forecaster,
        y                     = y,
        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,
        exog                  = exog,
        refit                 = refit,
        return_best           = return_best,
        verbose               = verbose
    )

    return results