1. Example 16.2a Moving Averages

2. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b DOW.XLS n We again look at the Dow Jones monthly data from January 1988 through March 1992 contained in this file. n How well do moving averages track this series when the span is 23 months; when the span is 12 months? n What about future forecasts, that is, beyond March 1992?

3. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages n Perhaps the simplest and one of the most frequently used extrapolation methods is the method of moving averages. n To implement the moving averages method, we first choose a span, the number of terms in each moving average. n The role of span is very important. If the span is large - say 12 months - then many observations go into each average, and extreme values have relatively little effect on the forecasts.

4. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages -- continued n The resulting series forecasts will be much smoother than the original series. n For this reason the moving average method is called a smoothing method.

5. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages Method in Excel n Although the moving averages method is quite easy to implement with Excel, it can be tedious. n Therefore we can use the Forecasting procedure of StatPro. This procedure lets us forecast with many methods. n We’ll go through the entire procedure step by step.

6. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Forecasting Procedure n To use the StatPro Forecasting procedure, the cursor needs to be in a data set with time series data. n We use the StatPro/Forecasting menu item and eventually choose Dow as the variable to analyze. n We then see several dialog boxes, the first of which is where we specify the timing.

7. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Timing Dialog Box n In the next dialog box, we specify which forecasting method to use and any parameters of that method.

8. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Method Dialog Box n We next see a dialog box that allows us to request various time series plots, and finally we get the usual choice of where to report the output.

9. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b The Output n The output consists of several parts. n First, the forecasts and forecast errors are shown for the historical period of data. n Actually, with moving averages we lose some forecasts at the beginning of the period. n If we ask for future forecasts, they are shown in red at the bottom of the data series. n There are no forecast errors and to the left we see the summary measures.

10. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages with Output Span 3

11. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages with Output Span 12

12. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b The Output -- continued n The essence of the forecasting method is very simple and is captured in column F of the output. It used the formula =AVERAGE($E2:$E4) in cell F5, which is then copied down.

13. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b The Plots n The plots show the behavior of the forecasts. n The forecasts with span 3 appear to track the data better, whereas the forecasts with span 12 is considerably smoother - it reacts less to ups and downs of the series.

14. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages Forecasts with Span 3

15. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b Moving Averages with Forecasts Span 12

16. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.7 | 16.7a | 16.7b16.1a16.216.316.416.516.616.7 16.7a16.7b In Summary n The summary measures MAE, RMSE, and MAPE confirm that moving averages with span 3 forecast the known observations better. n For example, the forecasts are off by about 3.6% with span 3, versus 7.7% with span 12. n Nevertheless, there is no guarantee that a span of 3 is better for forecasting future observations.