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T18-08 Calculate MAD, MSE

Purpose Allows the analyst to create and analyze the MAD and MSE for a forecast. A graphical representation of history and forecast are shown.

Inputs Historical Period DemandForecast

Outputs Forecast ErrorMAD & MSEGraph showing Historical Demand and Forecast

Limitations 60 Time Series Observations

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tat timeForecast F

tat time demand historical Actual A where

F A Error Forecast

t

t

tt

Given that a forecast is rarely correct, the methodology you choose should be the one which provides the least error from the actual historical demand. Forecast error is defined as the difference between actual historical demand and the forecast.

Forecast Accuracy

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14

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0 1 2 3 4 5 6 7 8 9 10 11 12

2

11

Forecast Error

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There are two measures used to monitor the accuracy of a forecast. The Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE).

The MAD is the average of the absolute value of the forecast errors. The MSE is the average of the squared forecast errors.

Note: The formula for the MSE shown above may vary slightly. Some textbooks divide the sum of the squared errors by n-1 rather than n.

2)( average MSE

)abs( average MAD

Monitoring the Forecast

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Example

Calculate the MAD and MSE for this forecast and show a graphical display of the history and forecast on the same graph.

Historical Demand Forecast

217 215213 216216 215210 214213 211219 214216 217212 216

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Input the History Values and Forecast in the light green cells.

The Error, MAD, and MSE are automatically calculated.

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A graph showing the History Values and Forecast is automatically produced.