Metric
MeanArctangentAbsolutePercentageError
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).
Schnellstart
python
from sktime.performance_metrics.forecasting import MeanArctangentAbsolutePercentageError
estimator = MeanArctangentAbsolutePercentageError(multioutput='uniform_average', multilevel='uniform_average', relative_to='y_true', eps=None, by_index=False)Parameter(5)
- 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.
Referenzen
- Kim, S., & Kim, H. (2016). “A new metric of absolute percentage error for intermittent demand forecasts”. International Journal of Systems Science.