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Metric

MeanSquaredPercentageError

API referenceSource
Multivariate

Mean squared percentage error (MSPE), or RMSPE, or symmetric MSPE, RMSPE.

Quickstart

python
from sktime.performance_metrics.forecasting import MeanSquaredPercentageError

estimator = MeanSquaredPercentageError(multioutput='uniform_average', multilevel='uniform_average', symmetric=False, square_root=False, by_index=False, relative_to='y_true', eps=None)

Parameters(7)

symmetricbool, default = False
Whether to calculate the symmetric version of the percentage metric
relative_to{“y_true”, “y_pred”}, default=”y_true”

Determines the denominator of the percentage error.

  • If "y_true", the denominator is the true values,

  • If "y_pred", the denominator is the predicted values.

square_rootbool, default = False
Whether to take the square root of the metric
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 MeanSquaredPercentageError
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> mspe = MeanSquaredPercentageError (symmetric = False)
>>> mspe (y_true, y_pred) np.float64(0.23776218820861678)
>>> smspe = MeanSquaredPercentageError (square_root = True, symmetric = False)
>>> smspe (y_true, y_pred) np.float64(0.48760864246710883)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> mspe (y_true, y_pred) np.float64(0.5080309901738473)
>>> smspe (y_true, y_pred) np.float64(0.7026794936195895)
>>> mspe = MeanSquaredPercentageError (multioutput = 'raw_values', symmetric = False)
>>> mspe (y_true, y_pred) array([0.34013605, 0.67592593])
>>> smspe = MeanSquaredPercentageError (multioutput = 'raw_values', symmetric = False, square_root = True)
>>> smspe (y_true, y_pred) array([0.58321184, 0.82214714])
>>> mspe = MeanSquaredPercentageError (multioutput = [0.3, 0.7 ], symmetric = False)
>>> mspe (y_true, y_pred) np.float64(0.5751889644746787)
>>> smspe = MeanSquaredPercentageError (multioutput = [0.3, 0.7 ], symmetric = False, square_root = True)
>>> smspe (y_true, y_pred) np.float64(0.7504665536595034)

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.