﻿

# Mean absolute scaled error

In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts . It was proposed in 2006 by Australian statistician Rob Hyndman, who described it as a "generally applicable measurement of forecast accuracy without the problems seen in the other measurements."[1]

The mean absolute scaled error is given by

$\mathrm{MASE} = \frac{1}{n}\sum_{t=1}^n\left( \left|\frac{e_t}{\frac{1}{n-1}\sum_{i=2}^n \left| Y_i-Y_{i-1}\right|}\right| \right)$[2]

where the numerator et is the forecast error for a given period, defined as the actual value (Yt) minus the forecast value (Ft) for that period: et = Yt − Ft, and the denominator is the average forecast error of the one-step "naive forecast method", which uses the actual value from the prior period as the forecast: Ft = Yt−1[3]

This scale-free error metric "can be used to compare forecast methods on a single series and also to compare forecast accuracy between series. This metric is well suited to intermittent-demand series[clarification needed] because it never gives infinite or undefined values[1] except in the irrelevant case where all historical data are equal.[2]

## References

1. ^ a b Hyndman, R. J. (2006). "Another look at measures of forecast accuracy", FORESIGHT Issue 4 June 2006, pg46 [1]
2. ^ a b Hyndman, R. J. and Koehler A. B. (2006). "Another look at measures of forecast accuracy." International Journal of Forecasting volume 22 issue 4, pages 679-688. doi:http://dx.doi.org/10.1016/j.ijforecast.2006.03.001
3. ^ Hyndman, Rob et al, Forecasting with Exponential Smoothing: The State Space Approach, Berlin: Springer-Verlag, 2008. ISBN 978-3-540-71916-8.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Mean absolute error — In statistics, the mean absolute error (MAE) is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by As the name suggests, the mean absolute error is an average of the… …   Wikipedia

• Mase — This article is about a musical artist. For the village in Switzerland, see Mase, Switzerland. For measure of accuracy, see Mean absolute scaled error. Mase Birth name Mason Derelle Betha Also known as Murda Ma\$e Born August 27, 1978 (1978 08 27 …   Wikipedia

• List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

• Variance — In probability theory and statistics, the variance of a random variable, probability distribution, or sample is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value (mean). Whereas… …   Wikipedia

• Malmquist bias — For other uses of Malmquist, see Malmquist (disambiguation). The Malmquist bias refers to an effect in observational astronomy which leads to the preferential detection of intrinsically bright objects. It was first popularized in 1922 by Swedish… …   Wikipedia

• Importance sampling — In statistics, importance sampling is a general technique for estimating the properties of a particular distribution, while only having samples generated from a different distribution rather than the distribution of interest. Depending on the… …   Wikipedia

• Normal distribution — This article is about the univariate normal distribution. For normally distributed vectors, see Multivariate normal distribution. Probability density function The red line is the standard normal distribution Cumulative distribution function …   Wikipedia

• Rounding — This article is about numerical rounding. For lip rounding in phonetics, see Labialisation. For other uses, see Rounding (disambiguation). Rounding a numerical value means replacing it by another value that is approximately equal but has a… …   Wikipedia

• Field electron emission — It is requested that a diagram or diagrams be included in this article to improve its quality. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. Field emission (FE) (also known as field… …   Wikipedia

• Thermodynamic temperature — is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its null or zero point …   Wikipedia

### Share the article and excerpts

Do a right-click on the link above