median_relative_absolute_error

median_relative_absolute_error(y_true, y_pred, horizon_weight=None, multioutput='uniform_average', **kwargs)

Median relative absolute error (MdRAE).

In relative error metrics, relative errors are first calculated by scaling (dividing) the individual forecast errors by the error calculated using a benchmark method at the same index position. If the error of the benchmark method is zero then a large value is returned.

MdRAE applies medan absolute error (MdAE) to the resulting relative errors.

Parameters:

y_truepd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Ground truth (correct) target values.

y_predpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Forecasted values.

y_pred_benchmarkpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon, default=None

Forecasted values from benchmark method.

horizon_weightarray-like of shape (fh,), default=None

Forecast horizon weights.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines how to aggregate metric for multivariate (multioutput) data. If array-like, values used as weights to average the errors. If ‘raw_values’, returns a full set of errors in case of multioutput input. If ‘uniform_average’, errors of all outputs are averaged with uniform weight.

Returns:

lossfloat

MdRAE loss. If multioutput is ‘raw_values’, then MdRAE is returned for each output separately. If multioutput is ‘uniform_average’ or an ndarray of weights, then the weighted average MdRAE of all output errors is returned.

See also

mean_relative_absolute_error

geometric_mean_relative_absolute_error

geometric_mean_relative_squared_error

References

Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.

Examples

>>> from aeon.performance_metrics.forecasting import         median_relative_absolute_error
>>> y_true = np.array([3, -0.5, 2, 7, 2])
>>> y_pred = np.array([2.5, 0.0, 2, 8, 1.25])
>>> y_pred_benchmark = y_pred*1.1
>>> median_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark)
1.0
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> y_pred_benchmark = y_pred*1.1
>>> median_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark)
0.6944444444444443
>>> median_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark, multioutput='raw_values')
array([0.55555556, 0.83333333])
>>> median_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark, multioutput=[0.3, 0.7])
0.7499999999999999