Mean absolute percentage error

Mean absolute percentage error (MAPE) is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage, and is defined by the formula:

\mbox{M} = \frac{1}{n}\sum_{t=1}^n \left| \frac{A_t-F_t}{A_t}\right|

where At is the actual value and Ft is the forecast value.

The difference between At and Ft is divided by the actual value At again. The absolute value of this calculation is summed for every fitted or forecast point in time and divided again by the number of fitted points n. This makes it a percentage error so one can compare the error of fitted time series that differ in level.

Although the concept of MAPE sounds very simple and convincing, it has two major drawbacks in practical application:

  • If there are zero values (which sometimes happens for example in demand series) there will be a division by zero
  • When having a perfect fit, MAPE is zero. But in regard to its upper level the MAPE has no restriction. When calculating the average MAPE for a number of time series there might be a problem: a few number of series that have a very high MAPE might distort a comparison between the average MAPE of time series fitted with one method compared to the average MAPE when using another method. In order to avoid this problem other measures have been defined, for example the sMAPE (symmetrical MAPE), weighted absolute percentage error (WAPE), real aggregated percentage error (RAPE),or a relative measure of accuracy (ROMA).

See also


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • 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… …   Wikipedia

  • Mean squared error — In statistics, the mean squared error (MSE) of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function,… …   Wikipedia

  • Mean — This article is about the statistical concept. For other uses, see Mean (disambiguation). In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). the expected value of a… …   Wikipedia

  • Margin of error — This article is about the statistical precision of estimates from sample surveys. For safety margins in engineering, see Factor of safety. For tolerance in engineering, see Tolerance (engineering). Not to be confused with Margin for Error. The… …   Wikipedia

  • MAPE — mean absolute percentage error …   Medical dictionary

  • MAPE — • mean absolute percentage error …   Dictionary of medical acronyms & abbreviations

  • 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

  • List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia

  • Forecasting — is the process of estimation in unknown situations. Prediction is a similar, but more general term. Both can refer to estimation of time series, cross sectional or longitudinal data. Usage can differ between areas of application: for example in… …   Wikipedia

  • Forecast — Die Prognose (griechisch, πρóγνωσις – wörtlich „das Vorwissen“, die „Voraus Kenntnis“), deutsch Vorhersage oder Voraussage, selten auch: Prädiktion (lat. praedicare „ im Voraus“ und „sagen“) bezeichnet die Aussagen über Ereignisse, Zustände oder… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.