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Metric

MeanSquaredPercentageError

API referenceSource
Multivariate

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

If square_root is False then calculates MSPE and if square_root is True then calculates root mean squared percentage error (RMSPE). If symmetric is True then calculates sMSPE or sRMSPE. Output is non-negative floating point. The best value is 0.0.

MSPE is measured in squared percentage error relative to the test data and RMSPE is measured in percentage error relative to the test data. Because the calculation takes the square rather than absolute value of the percentage forecast error, large errors are penalized more than MAPE, sMAPE, MdAPE or sMdAPE.

There is no limit on how large the error can be, particularly when y_true values are close to zero. In such cases the function returns a large value instead of inf.

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.