THE SPECIALIST WITH A UNIVERSAL MIND

Teaching Forecasting

by Andrew Vazsonyi, University of San Francisco

John Hanke, Eastern Washington University, chaired an interesting session on this topic at the Western Decision Sciences Institute meeting on April 2, 1994. I discussed the topic with some colleagues and, apparently, there is much room for improvement in teaching forecasting.

The first thing to do when forecasting is to find out what managers will do with the forecast. This leads immediately to the basic question: What do they want to forecast? There seems to be a hidden assumption in our textbooks that management wants to forecast sales. However, in reality, we forecast demand, and the two are not the same.

Typically, firms have data on past sales, but not necessarily on demand. In many practical situations, it is very difficultþor impracticalþto get data on demand. Often, only by managerial judgment can sales be translated into demand. Moreover, sales depend not only on demand but on many other factors.

Suppose the firm is planning the manufacture of widgets, and the issue is to determine the quantity Q to be made. If the forecast F were absolutely correct, the firm would probably set Q to F. However, due to uncertainty, this is not the case.

Suppose we measure uncertainty by the standard deviation of the forecast distribution. Then presumably the quantity made would be a function of F and : Q(f, <$sigma>), and the firm would choose the forecasting model that maximizes the expected profit. However, forecasting systems typically minimize the RMS error, which is only loosely related to profit maximization. Thus, comparing different types of time-series analysis by RMS may lead to erroneous results.

If we want to teach forecasting in a meaningful way, we need to explain these complicating factors and stress the importance of applying judgment to the problem. The most powerful way to do this is to use graphic analysis, and fortunately spreadsheets provide a way to relate analysis and judgment pictorially.

The simplest example is the cleaning up of data. Visual inspection of data is easy with spreadsheets and probably more useful than using elaborate mathematical techniques. Also the human eye is good in the search for leading indicators.

The other important graphic analysis is eye-balling trend lines. Visual analysis of curve fitting is basic, and regression analysis, exponential smoothing, and time-series analysis, all help in selecting an appropriate forecasting model.

Explaining and visualizing seasonal variations, and separating trend from cyclic fluctuations is more difficult. Traditional decomposition models are hard to understand and applying judgment becomes difficult and often impossible. I have been experimenting with spreadsheets to visualize forecasting where there is trend and seasonal variation.

Exhibit 1 shows an ideal trend and cycles. Exhibit 2 shows the pie chart of seasonal fluctiuation. The first problem is to set the parameters of the pie chart (12 parameters to be normalized for the 12 months) so the model gives a good fit for the data. The second problem is to set the parameters of the trend line. This can be visualized by using the Archimedes spiral shown in Exhibit 3, using polar coordinates. The forecast is measured by R, the distance from the origin, and time by the angle from the x axis. If there is no growth, the spiral degenerates into a single closed curve; if there is no cyclic component, the Archimedes spiral itself represents growth. When there is seasonal fluctuation, the pie chart and the spiral must be combined as shown in Exhibit 4. It can be readily seen, for example, that July sales are high, and there is a dip each April.

You can visualize the problem as fitting a pie chart and a modified Archimedes spiral to the given data. The pie chart when normalized has 11 parameters; the number of parameters of the trend line depends on which trend you use. Linear or exponential growth requires two parameters. So the problem is to fit the composite curve to the data by setting these parameters so that the expected profit is maximized.

I created the charts by using a parametric spreadsheet. I assumed a linear growth, and used 12 parameters for the pie chart, and two parameters for the growth. I used imbedded charts, and so could change any of the parameters and watch how the fit changes. If you assume a profit function, the expected profit can be automatically calculated. You can assume any set of historical data, any forecasting model, mathematical or judgmental, and see how the charts and expected profit unfold.

I have not yet tried this approach in class, but feel it has merit. The issue is psychological and depends on the mathematical sophistication of the students. I will be interested in communicating with you in further development and testing of the model.

FOR COPIES OF FIGURES, contact the Managing Editor at dsihhj@gsusgi2.gsu.edu.

Write, call, or fax to my home:
ANDREW VAZSONYI
156 Oak Island Dr.
Santa Rosa, CA 95409
(707) 539-0272
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