Chapter 11 Times Series 451The square root of the MSE gives us the standard error, which indicates
the magnitude of the typical forecasted error. A standard error of 5 would
indicate that the forecasts are typically off by about 5 points.
Another way of measuring the magnitude is to take the sum of the abso-
lute values of the differences between the forecasted and observed values.
This measure, called the mean absolute deviation (MAD), has the formula
MAD 5
an
t 51 `yt^2 y^t`n
One of the differences between the MAD and the MSE is that the MAD
does not penalize a forecast as much for very large errors. Because the MSE
squares the deviations, large errors become even more prominent.
Another measure is the mean absolute percent error (MAPE), which ex-
presses the accuracy as a percentage of the observed value. The formula for
the MAPE is
MAPE 5
an
t 51 `(^1) yt 2 y^t (^2) /yt`
n
3100
To help you get a visual image of the impact that differing values of w
have on smoothing the data and forecasting the next value in the series, you
can open the Exponential Smoothing workbook.
CONCEPT TUTORIALS
One-Parameter Exponential Smoothing
To use the Exponential Smoothing workbook:1 Open the Exponential Smoothing workbook from the Explore folder.
Enable the macros in the workbook.
2 Review the contents of the workbook up to the section entitled
Explore One-Parameter Exponential Smoothing. The worksheet is
shown in Figure 11-12.