Example of Double Exponential Smoothingmain topic interpreting results session command see also
Example of Double Exponential SmoothingYou wish to predict employment over six months in a segment of the metals industry. You use double exponential smoothing as there is no clear trend or seasonal pattern in the data, and you want to compare the fit by this method with that from single exponential smoothing (see Example of single exponential smoothing).
1 Open the worksheet EMPLOY.MTW.
2 Choose Stat > Time Series > Double Exp Smoothing.
3 In Variable, enter Metals.
4 Check Generate forecasts and enter 6 in Number of forecasts. Click OK.
Session window output
Double Exponential Smoothing for Metals
Data Metals Length 60
Smoothing Constants
α (level) 1.03840 γ (trend) 0.02997
Accuracy Measures
MAPE 1.19684 MAD 0.54058 MSD 0.46794
Forecasts
Period Forecast Lower Upper 61 48.0961 46.7718 49.4205 62 48.1357 46.0600 50.2113 63 48.1752 45.3135 51.0368 64 48.2147 44.5546 51.8747 65 48.2542 43.7899 52.7184 66 48.2937 43.0221 53.5652 |
Graph window output
Minitab generated the default time series plot which displays the series and fitted values (one-step-ahead forecasts), along with the six forecasts.
In both the Session and Graph windows, Minitab displays the smoothing constants (weights) for the level and trend components and three measures to help you determine the accuracy of the fitted values: MAPE, MAD, and MSD (see Measures of accuracy).
The three accuracy measures, MAPE, MAD, and MSD, were respectively 1.19684, 0.54058, and 0.46794 for double exponential smoothing fit, compared to 1.11648, 0.50427, and 0.42956 for the single exponential smoothing fit (see Example of single exponential smoothing). Because these values are smaller for single exponential smoothing, you can judge that this method provides a slightly better fit to these data.
Because the difference in accuracy measures for the two exponential smoothing methods are small, you might consider the type of forecast (horizontal line versus line with slope) in selecting between methods. Double exponential smoothing forecasts an employment pattern that is slightly increasing though the last four observations are decreasing. A higher weight on the trend component can result in a prediction in the same direction as the data, which may be more realistic, but the measured fit may not be as good as when Minitab generated weights are used.