MeanArctangentAbsolutePercentageError

class MeanArctangentAbsolutePercentageError(multioutput='uniform_average', multilevel='uniform_average', relative_to='y_true', eps=None, by_index=False)[source]

Mean Arctangent Absolute Percentage Error (MAAPE).

MAAPE is a variation of the Mean Absolute Percentage Error (MAPE) that is robust to zero values in the ground truth series. While MAPE is undefined when y_true=0, MAAPE uses the arctangent function to bound the error.

The formula is defined as:

\[\text{MAAPE} = \frac{1}{n} \sum_{t=1}^{n} \arctan \left( \left| \frac{y_t - \hat{y}_t}{y_t} \right| \right)\]

where \(y_t\) is the actual value and \(\hat{y}_t\) is the forecast value.

The result is bounded between 0 and \(\pi/2\) (approx 1.57).

Parameters:

multioutput{‘raw_values’, ‘uniform_average’}, default=’uniform_average’: Defines aggregating of multiple output values.
multilevel{‘raw_values’, ‘uniform_average’}, default=’uniform_average’: Defines aggregating of multiple hierarchical levels.
relative_to{“y_true”, “y_pred”}, default=”y_true”: Determines the denominator of the percentage error.
epsfloat, default=None: Numerical epsilon used in denominator to avoid division by zero.
by_indexbool, default=False: If True, return the metric value at each time point. If False, return the aggregate metric value.

References

Kim, S., & Kim, H. (2016). “A new metric of absolute percentage error for intermittent demand forecasts”. International Journal of Systems Science.

Methods

__call__(y_true, y_pred, **kwargs)

Calculate metric value using underlying metric function.

__call__(y_true, y_pred, **kwargs)[source]

Calculate metric value using underlying metric function.

Parameters:

y_truetime series in sktime compatible data container format.

Ground truth (correct) target values.

Individual data formats in sktime are so-called mtype specifications, each mtype implements an abstract scitype.

Series scitype = individual time series, vanilla forecasting. pd.DataFrame, pd.Series, or np.ndarray (1D or 2D)
Panel scitype = collection of time series, global/panel forecasting. pd.DataFrame with 2-level row MultiIndex (instance, time), 3D np.ndarray (instance, variable, time), list of Series typed pd.DataFrame
Hierarchical scitype = hierarchical collection, for hierarchical forecasting. pd.DataFrame with 3 or more level row MultiIndex (hierarchy_1, ..., hierarchy_n, time)

For further details on data format, see glossary on mtype. For usage, see forecasting tutorial examples/01_forecasting.ipynb

y_predtime series in sktime compatible data container format

Predicted values to evaluate against ground truth. Must be of same format as y_true, same indices and columns if indexed.

y_pred_benchmarkoptional, time series in sktime compatible data container format

Benchmark predictions to compare y_pred to, used for relative metrics. Required only if metric requires benchmark predictions, as indicated by tag requires-y-pred-benchmark. Otherwise, can be passed to ensure interface consistency, but is ignored. Must be of same format as y_true, same indices and columns if indexed.

y_trainoptional, time series in sktime compatible data container format

Training data used to normalize the error metric. Required only if metric requires training data, as indicated by tag requires-y-train. Otherwise, can be passed to ensure interface consistency, but is ignored. Must be of same format as y_true, same columns if indexed, but not necessarily same indices.

sample_weightoptional, 1D array-like, or callable, default=None

Sample weights for each time point.

If None, the time indices are considered equally weighted.
If an array, must be 1D. If y_true and y_pred``are a single time series, ``sample_weight must be of the same length as y_true. If the time series are panel or hierarchical, the length of all individual time series must be the same, and equal to the length of sample_weight, for all instances of time series passed.
If a callable, it must follow SampleWeightGenerator interface, or have one of the following signatures: y_true: pd.DataFrame -> 1D array-like, or y_true: pd.DataFrame x y_pred: pd.DataFrame -> 1D array-like.

Returns:

lossfloat, np.ndarray, or pd.DataFrame

Calculated metric, averaged or by variable. Weighted by sample_weight if provided.

float if multioutput="uniform_average" or array-like, and ``multilevel="uniform_average" or “uniform_average_time”``. Value is metric averaged over variables and levels (see class docstring)
np.ndarray of shape (y_true.columns,) if multioutput=”raw_values”` and multilevel="uniform_average" or "uniform_average_time". i-th entry is the, metric calculated for i-th variable
pd.DataFrame if multilevel="raw_values". of shape (n_levels, ), if multioutput="uniform_average"; of shape (n_levels, y_true.columns) if multioutput="raw_values". metric is applied per level, row averaging (yes/no) as in multioutput.