Mean Absolute Deviation

Mean Absolute Deviation (MAD) is the mean (or average) of the absolute values (or magnitude) of the deviations (or errors) between actual and forecast data. MAD is a measure of the average magnitude of errors to expect, given a forecasting method and data history. Because absolute values are used in the calculation, positive errors do not cancel out negative errors. When comparing several forecasting methods, the one with the smallest MAD is the most reliable for that product for that holdout period. When the forecast is unbiased and errors are normally distributed, a simple mathematical relationship exists between MAD and two other common measures of distribution, which are standard deviation and Mean Squared Error. For example:

• MAD = (Σ | (Actual) – (Forecast)|)n

• Standard Deviation, (σ) ≅ 1.25 MAD

• Mean Squared Error ≅ –σ2

This example indicates the calculation of MAD for two of the forecasting methods. This example assumes that you have specified in the processing option that the holdout period length (periods of best fit) is equal to five periods.