Metrics

skforecast.metrics.mean_absolute_scaled_error

mean_absolute_scaled_error(y_true, y_pred, y_train)

Mean Absolute Scaled Error (MASE)

MASE is a scale-independent error metric that measures the accuracy of a forecast. It is the mean absolute error of the forecast divided by the mean absolute error of a naive forecast in the training set. The naive forecast is the one obtained by shifting the time series by one period. If y_train is a list of numpy arrays or pandas Series, it is considered that each element is the true value of the target variable in the training set for each time series. In this case, the naive forecast is calculated for each time series separately.

Parameters:

Name	Type	Description	Default
y_true	pandas Series, numpy ndarray	True values of the target variable.	required
y_pred	pandas Series, numpy ndarray	Predicted values of the target variable.	required
y_train	list, pandas Series, numpy ndarray	True values of the target variable in the training set. If list, it is consider that each element is the true value of the target variable in the training set for each time series.	required

Returns:

Name	Type	Description
mase	float	MASE value.

Source code in skforecast\metrics\metrics.py

def mean_absolute_scaled_error(
    y_true: Union[pd.Series, np.ndarray],
    y_pred: Union[pd.Series, np.ndarray],
    y_train: Union[list, pd.Series, np.ndarray],
) -> float:
    """
    Mean Absolute Scaled Error (MASE)

    MASE is a scale-independent error metric that measures the accuracy of
    a forecast. It is the mean absolute error of the forecast divided by the
    mean absolute error of a naive forecast in the training set. The naive
    forecast is the one obtained by shifting the time series by one period.
    If y_train is a list of numpy arrays or pandas Series, it is considered
    that each element is the true value of the target variable in the training
    set for each time series. In this case, the naive forecast is calculated
    for each time series separately.

    Parameters
    ----------
    y_true : pandas Series, numpy ndarray
        True values of the target variable.
    y_pred : pandas Series, numpy ndarray
        Predicted values of the target variable.
    y_train : list, pandas Series, numpy ndarray
        True values of the target variable in the training set. If `list`, it
        is consider that each element is the true value of the target variable
        in the training set for each time series.

    Returns
    -------
    mase : float
        MASE value.

    """

    if not isinstance(y_true, (pd.Series, np.ndarray)):
        raise TypeError("`y_true` must be a pandas Series or numpy ndarray.")
    if not isinstance(y_pred, (pd.Series, np.ndarray)):
        raise TypeError("`y_pred` must be a pandas Series or numpy ndarray.")
    if not isinstance(y_train, (list, pd.Series, np.ndarray)):
        raise TypeError("`y_train` must be a list, pandas Series or numpy ndarray.")
    if isinstance(y_train, list):
        for x in y_train:
            if not isinstance(x, (pd.Series, np.ndarray)):
                raise TypeError(
                    ("When `y_train` is a list, each element must be a pandas Series "
                     "or numpy ndarray.")
                )
    if len(y_true) != len(y_pred):
        raise ValueError("`y_true` and `y_pred` must have the same length.")
    if len(y_true) == 0 or len(y_pred) == 0:
        raise ValueError("`y_true` and `y_pred` must have at least one element.")

    if isinstance(y_train, list):
        naive_forecast = np.concatenate([np.diff(x) for x in y_train])
    else:
        naive_forecast = np.diff(y_train)

    mase = np.mean(np.abs(y_true - y_pred)) / np.nanmean(np.abs(naive_forecast))

    return mase

skforecast.metrics.root_mean_squared_scaled_error

root_mean_squared_scaled_error(y_true, y_pred, y_train)

Root Mean Squared Scaled Error (RMSSE)

RMSSE is a scale-independent error metric that measures the accuracy of a forecast. It is the root mean squared error of the forecast divided by the root mean squared error of a naive forecast in the training set. The naive forecast is the one obtained by shifting the time series by one period. If y_train is a list of numpy arrays or pandas Series, it is considered that each element is the true value of the target variable in the training set for each time series. In this case, the naive forecast is calculated for each time series separately.

Parameters:

Name	Type	Description	Default
y_true	pandas Series, numpy ndarray	True values of the target variable.	required
y_pred	pandas Series, numpy ndarray	Predicted values of the target variable.	required
y_train	list, pandas Series, numpy ndarray	True values of the target variable in the training set. If list, it is consider that each element is the true value of the target variable in the training set for each time series.	required

Returns:

Name	Type	Description
rmsse	float	RMSSE value.

Source code in skforecast\metrics\metrics.py

def root_mean_squared_scaled_error(
    y_true: Union[pd.Series, np.ndarray],
    y_pred: Union[pd.Series, np.ndarray],
    y_train: Union[list, pd.Series, np.ndarray],
) -> float:
    """
    Root Mean Squared Scaled Error (RMSSE)

    RMSSE is a scale-independent error metric that measures the accuracy of
    a forecast. It is the root mean squared error of the forecast divided by
    the root mean squared error of a naive forecast in the training set. The
    naive forecast is the one obtained by shifting the time series by one period.
    If y_train is a list of numpy arrays or pandas Series, it is considered
    that each element is the true value of the target variable in the training
    set for each time series. In this case, the naive forecast is calculated
    for each time series separately.

    Parameters
    ----------
    y_true : pandas Series, numpy ndarray
        True values of the target variable.
    y_pred : pandas Series, numpy ndarray
        Predicted values of the target variable.
    y_train : list, pandas Series, numpy ndarray
        True values of the target variable in the training set. If list, it
        is consider that each element is the true value of the target variable
        in the training set for each time series.

    Returns
    -------
    rmsse : float
        RMSSE value.

    """

    if not isinstance(y_true, (pd.Series, np.ndarray)):
        raise TypeError("`y_true` must be a pandas Series or numpy ndarray.")
    if not isinstance(y_pred, (pd.Series, np.ndarray)):
        raise TypeError("`y_pred` must be a pandas Series or numpy ndarray.")
    if not isinstance(y_train, (list, pd.Series, np.ndarray)):
        raise TypeError("`y_train` must be a list, pandas Series or numpy ndarray.")
    if isinstance(y_train, list):
        for x in y_train:
            if not isinstance(x, (pd.Series, np.ndarray)):
                raise TypeError(
                    ("When `y_train` is a list, each element must be a pandas Series "
                     "or numpy ndarray.")
                )
    if len(y_true) != len(y_pred):
        raise ValueError("`y_true` and `y_pred` must have the same length.")
    if len(y_true) == 0 or len(y_pred) == 0:
        raise ValueError("`y_true` and `y_pred` must have at least one element.")

    if isinstance(y_train, list):
        naive_forecast = np.concatenate([np.diff(x) for x in y_train])
    else:
        naive_forecast = np.diff(y_train)

    rmsse = np.sqrt(np.mean((y_true - y_pred) ** 2)) / np.sqrt(np.nanmean(naive_forecast ** 2))

    return rmsse

skforecast.metrics.add_y_train_argument

add_y_train_argument(func)

Add y_train argument to a function if it is not already present.

Parameters:

Name	Type	Description	Default
func	callable	Function to which the argument is added.	required

Returns:

Name	Type	Description
wrapper	callable	Function with y_train argument added.

Source code in skforecast\metrics\metrics.py

def add_y_train_argument(func: Callable) -> Callable:
    """
    Add `y_train` argument to a function if it is not already present.

    Parameters
    ----------
    func : callable
        Function to which the argument is added.

    Returns
    -------
    wrapper : callable
        Function with `y_train` argument added.

    """

    sig = inspect.signature(func)

    if "y_train" in sig.parameters:
        return func

    new_params = list(sig.parameters.values()) + [
        inspect.Parameter("y_train", inspect.Parameter.KEYWORD_ONLY, default=None)
    ]
    new_sig = sig.replace(parameters=new_params)

    @wraps(func)
    def wrapper(*args, y_train=None, **kwargs):
        return func(*args, **kwargs)

    wrapper.__signature__ = new_sig

    return wrapper