Example 13.6a Houses Sold in the Midwest Exponential Smoothing

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Objective To see how well a simple exponential smoothing model, with an appropriate smoothing constant, fits the housing sales data, and to see how StatPro implements this method.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b The Problem n Previously, we used the moving averages method to forecast monthly housing sales in the Midwest. (See the HOUSESALES.XLS file)HOUSESALES.XLS n How well does simple exponential smoothing work with this data set? n What smoothing constant should we use?

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b StatPro’s Exponential Smoothing Model n We start by selecting the StatPro/Forecasting menu item. n We first specify that the data are monthly, beginning in January 1994, we do not hold out any of the data for validation, and we ask for 12 months of future forecasts. n We then fill out the next dialog box like this:

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Method Dialog Box n That is, we select the exponential smoothing option, elect the Simple option choose smoothing constant (0.1 was chosen here) and elect not to optimize, and specify that the data are not seasonal.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b StatPro’s Exponential Smoothing Model -- continued n On the next dialog sheet we ask for time series charts of the series with the forecasts superimposed and the series of forecast errors. n The results appear in the following three figures. n The heart of the method takes place in the columns F, G, and H of the first figure. The following formulas are used in row 6 of these columns. =Alpha*E6+(1-Alpha)*F5 =F5 =E6-G6

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b StatPro’s Exponential Smoothing Model -- continued n The one exception to this scheme is in row 2. –Every exponential smoothing method requires initial values, in this case the initial smoothed level in cell F2. –There is no way to calculate this value because the previous value is unknown. n Note that 12 future forecasts are all equal to the last calculated smoothed level in cell F90. –The fact that these remain constant is a consequence of the assumption behind simple exponential smoothing, namely, that the series is not really going anywhere. Therefore, the last smoothed level is the best indication of future values of the series we have.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Simple Exponential Smoothing Output

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Forecast Series & Error Charts n The next figure shows the forecast series superimposed on the original series. n We see the obvious smoothing effect of a relatively small alpha level. n The forecasts don’t track the series well; but if the zig zags are just random noise, then we don’t want the forecasts to track these random ups and downs too closely.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Plot of Forecasts from Simple Exponential Smoothing

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Summary Measures n The RMSE and MAE indicate that the forecast from this model are typically off by a magnitude of about 12 to 15 thousand, and the MAPE indicates that they are off by about 7.9%. n These imply fairly sizable errors. n One way to reduce the errors is to use a different smoothing method. n Another way is to use a different smoothing constant. There are two ways you can do this.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Summary Measures -- continued n First, you can simply enter different values in cell B6 of the table. All formulas, including those for MAE, EMSE and MAPE, will update automatically. n Second, you can check the Optimize with Solver box in the dialog box. This automatically runs the Excel Solver to find the smoothing constant that minimizes RMSE. n We tried this for the Housing data and obtained the forecasts shown on the next slide.

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Plot of Forecasts with an Optimal Smoothing Constant

| 13.1a | 13.2 | 13.3 | 13.4 | 13.5 | 13.5b | 13.6 | 13.7 | 13.7a | 13.7b13.1a b a13.7b Summary Measures -- continued n The corresponding MAE, RMSE, and MAPE are 11.4, 14.1 and 7.7 %, slightly better than before. n This larger smoothing constant produces a less smooth forecast curve and slightly better error measures. n However, there is no guarantee that future forecasts made with this optimal smoothing constant will be any better than with a smoothing constant of 0.1.