Example 13.6Houses Sold in the Midwest

Moving Averages

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Objective

To see whether a moving averages model with an appropriate span fits the housing sales data, and to see how StatPro implements this method.

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HOUSESALES.XLS

This file contains monthly data on the number of houses sold in the Midwest from January 1994 through May 2001.

A time series plot of the data appears on the next slide.

Does a moving averages model fit this data set well?

What span should be used?

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Time Series Plot of Monthly House Sales

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Moving Averages Perhaps the simplest and one of the most frequently

used extrapolation methods is the method of moving averages.

To implement the moving averages method, we first choose a span, the number of terms in each moving average.

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.

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Moving Averages -- continued

The resulting series forecasts will be much smoother than the original series.

For this reason the moving average method is called a smoothing method.

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Moving Averages Method in Excel Although the moving averages method is quite easy

to implement with Excel, it can be tedious.

Therefore we can use the Forecasting procedure of StatPro. This procedure lets us forecast with many methods.

We’ll go through the entire procedure step by step.

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Forecasting Procedure

To use the StatPro Forecasting procedure, the cursor needs to be in a data set with time series data.

We use the StatPro/Forecasting menu item and eventually choose Sales as the variable to analyze.

We then see several dialog boxes, the first of which is where we specify the timing.

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Timing Dialog Box

In the next dialog box, we specify which forecasting method to use and any parameters of that method.

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Method Dialog Box

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 .

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The Output The output consists of several parts, one for the span of 3 and

the other for span of 12.

First, the forecasts and forecast errors are shown for the historical period of data.

Actually, with moving averages we lose some forecasts at the beginning of the period.

If we ask for future forecasts, they are shown in red at the bottom of the data series.

There are no forecast errors and to the left we see the summary measures.

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Moving Averages with Output Span 3

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Moving Averages with Output Span 12

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The Output -- continued

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.

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The Plots

The plots show the behavior of the forecasts.

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.

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Moving Averages Forecasts with Span 3

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Moving Averages with Forecasts Span 12

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In Summary

The forecasted series with span 3 follows the ups and downs of the actual series fairly closely, whereas the forecasted series with span 12 is much smoother and doesn’t react nearly as much to these ups and downs.

Which of these is better? The error summary measures indicate that it is a virtual toss-up.

The MAPE with span 12 is slightly lower, indicated that these forecasts are off, on average, by about 8.1%, but the RMSE with span 3 is slightly lower.

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In Summary -- continued

At this point, it is up to the judgment of the forecaster, who presumably has some knowledge of the housing sales market in the Midwest.

If she believes that the ups and downs in the original series are largely unpredictable noise, then she will probably trust the smooth forecasts from a span of 12.

Otherwise, she might use a span of 3 or some other intermediate span.