Mean Absolute Percentage Error
Encyclopedia
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:
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:
The alternative MAPE definition:
Problems can occur when calculating the MAPE value with a serie of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error,caused by a small deviation in error, can occur.
The difference with the original formula is that each Actual Values (At) of the serie is replaced by the average Actual Value (Āt) of that serie. Hence, the distortions are smoothed out.
This alternative is still being used for measuring the performance of models that forecast spot electricity prices.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, specifically trending
Trend estimation
Trend estimation is a statistical technique to aid interpretation of data. When a series of measurements of a process are treated as a time series, trend estimation can be used to make and justify statements about tendencies in the data...
. It usually expresses accuracy as a percentage, and is defined by the formula:
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 errorReal aggregated percentage errorIn spectral analysis of time series data in statistics, mean absolute percentage error is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage...
(RAPE),or a relative measure of accuracy (ROMA).
The alternative MAPE definition:
Problems can occur when calculating the MAPE value with a serie of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error,caused by a small deviation in error, can occur.
The difference with the original formula is that each Actual Values (At) of the serie is replaced by the average Actual Value (Āt) of that serie. Hence, the distortions are smoothed out.
This alternative is still being used for measuring the performance of models that forecast spot electricity prices.
See also
- Least absolute deviationsLeast absolute deviationsLeast absolute deviations , also known as Least Absolute Errors , Least Absolute Value , or the L1 norm problem, is a mathematical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data...
- Mean absolute errorMean absolute errorIn statistics, the mean absolute error is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by...
- Symmetric mean absolute percentage errorSymmetric mean absolute percentage errorSymmetric mean absolute percentage error is an accuracy measure based on percentage errors. It is usually defined as follows:where At is the actual value and Ft is the forecast value....