MASE_nonseasonal: MASE_nonseasonal

In Mthrun/TSAT: Time Series Analysis Tools (TSAT)

MASE_nonseasonal

Description

Mean absolute scaled error (MASE)

Usage

MASE_nonseasonal(Y,For)

Arguments

Y	numerical vector of [1:n],n>1
For	numerical vector of [1:n],n>1

Details

The mean absolute scaled error has the following desirable properties:

1.) Symmetry error penalizes positive and negative forecast errors equally

penalizes errors in large forecasts and small forecasts equally

2.) Predictable behavior as y t->0: Percentage forecast accuracy measures such as the Mean absolute percentage error (MAPE) rely on division of y t skewing the distribution of the MAPE for values of y t near or equal to 0. This is especially problematic for data sets whose scales do not have a meaningful 0, such as temperature in Celsius or Fahrenheit, and for intermittent demand data sets, where y t = 0 occurs frequently.

3.) Interpretability: The mean absolute scaled error can be easily interpreted, as values greater than one indicate that in-sample one-step forecasts from the naïve method perform better than the forecast values under consideration.

4.) Asymptotic normality of the MASE: The Diebold-Mariano test for one-step forecasts is used to test the statistical significance of the difference between two sets of forecasts. To perform hypothesis testing with the Diebold-Mariano test statistic, it is desirable for DM ~ N(0,1), where DM is the value of the test statistic. The DM statistic for the MASE has been empirically shown to approximate this distribution, while the mean relative absolute error (MRAE), MAPE and sMAPE do not.

Value

MASE error value

Author(s)

Michael Thrun

References

Hyndman, R. J. (2006). "Another look at measures of forecast accuracy", FORESIGHT Issue 4 June 2006, p. 46

Examples

#usage with vectors, x forecast, y test data
x=c(100,110,95)
y=c(90,100,93)
MASE_nonseasonal(x,y)

Mthrun/TSAT documentation built on Feb. 5, 2024, 11:15 p.m.