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Metric

MeanAbsoluteScaledError

API referenceSource
Multivariate

Mean absolute scaled error (MASE).

Quickstart

python
from sktime.performance_metrics.forecasting import MeanAbsoluteScaledError

estimator = MeanAbsoluteScaledError(multioutput='uniform_average', multilevel='uniform_average', sp=1, by_index=False, eps=None)

Parameters(5)

spint, default = 1
Seasonal periodicity of the data
epsfloat, default=None
Numerical epsilon used in denominator to avoid division by zero. Absolute values smaller than eps are replaced by eps. If None, defaults to np.finfo(np.float64).eps
multioutput‘uniform_average’ (default), 1D array-like, or ‘raw_values’

Whether and how to aggregate metric for multivariate (multioutput) data.

  • If 'uniform_average' (default), errors of all outputs are averaged with uniform weight.

  • If 1D array-like, errors are averaged across variables, with values used as averaging weights (same order).

  • If 'raw_values', does not average across variables (outputs), per-variable errors are returned.

multilevel{‘raw_values’, ‘uniform_average’, ‘uniform_average_time’}

How to aggregate the metric for hierarchical data (with levels).

  • If 'uniform_average' (default), errors are mean-averaged across levels.

  • If 'uniform_average_time', metric is applied to all data, ignoring level index.

  • If 'raw_values', does not average errors across levels, hierarchy is retained.

by_indexbool, default=False

Controls averaging over time points in direct call to metric object.

  • If False (default), direct call to the metric object averages over time points, equivalent to a call of the evaluate method.

  • If True, direct call to the metric object evaluates the metric at each time point, equivalent to a call of the evaluate_by_index method.

Examples

>>> import numpy as np
>>> from sktime.performance_metrics.forecasting import MeanAbsoluteScaledError
>>> y_train = np. array ([5, 0.5, 4, 6, 3, 5, 2 ])
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> mase = MeanAbsoluteScaledError ()
>>> mase (y_true, y_pred, y_train = y_train) np.float64(0.18333333333333335)
>>> y_train = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> mase (y_true, y_pred, y_train = y_train) np.float64(0.18181818181818182)
>>> mase = MeanAbsoluteScaledError (multioutput = 'raw_values')
>>> mase (y_true, y_pred, y_train = y_train) array([0.10526316, 0.28571429])
>>> mase = MeanAbsoluteScaledError (multioutput = [0.3, 0.7 ])
>>> mase (y_true, y_pred, y_train = y_train) np.float64(0.21935483870967742)

References

  1. Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4. Hyndman, R. J. (2006). “Another look at forecast accuracy metrics for intermittent demand”, Foresight, Issue 4. Makridakis, S., Spiliotis, E. and Assimakopoulos, V. (2020) “The M4 Competition: 100,000 time series and 61 forecasting methods”, International Journal of Forecasting, Volume 3.