Using Seasonal Simplification to Improve Forecasts

Forecast Pro includes a forecasting approach called seasonal simplification. Seasonal simplification is an extension of exponential smoothing which “simplifies” the modeling of the seasonal pattern by reducing the number of indices used. In many cases the seasonally simplified model can substantially improve forecast accuracy.


Figure 1: Weekly beer sales

Figure 2: Monthly beer sales

Consider the data shown above. Figure 1 shows the demand history for weekly sales of beer (in green) and the forecasts generated by a traditional Winters model (in red). Figure 2 shows the same data on a monthly basis forecasted using a traditional Winters model. Notice how “rough” the weekly forecasts are and how the direction changes virtually every week. Some of this can be attributed to holidays and other recurring events; however, most of it is not plausible. Contrast the roughness of the weekly forecasts with the smoothness of the monthly forecasts—they go down in the winter and up in the summer—just as you’d expect.

The problem is that a traditional Winters exponential smoothing model uses 52 indices to capture a weekly seasonal pattern. This is a very complex model of the seasonality. If the structure of the data cannot support this complexity, the model will not forecast well.

Seasonal simplification addresses this issue by allowing you to use fewer than 52 indices to model a weekly seasonal pattern. This will improve the forecasts in cases where the structure in the data cannot support using the full set of indices.

The approach is very straightforward. Essentially, the seasonal indices are replaced with a lesser number of event indices. Let’s illustrate this with an example.

A traditional seasonal exponential smoothing model for a weekly data set generates 52 seasonal indices—one for each week. You could replicate this model exactly by building a “nonseasonal” smoothing model with an event schedule that used 52 event types to map each week of the year into its own “bucket”. The resulting model would have 52 “event” indices; however, since the schedule mapped each week into one of 52 buckets, the indices are exactly the same as those generated in the “seasonal” model.

Now what if we used this event approach but rather than using 52 buckets we used 26, placing the first two weeks of the year in “bucket 1”, the next two weeks in “bucket 2”, the two weeks following that in “bucket 3”, etc.? The result would be a model with 26 “event” indices. These 26 indices would be used to capture a simplified seasonal pattern. We refer to this model as a seasonally simplified model with 26 indices per year and a bucket size equal to 2 (i.e., we are assigning each two week period per year into its own bucket). If we elected to map every four weeks into its own bucket (i.e., bucket size=4) we would generate 13 indices and simplify the seasonality even further.

Figure 3

Figure 3 shows the forecasts generated for our beer data set using a seasonally simplified model with bucket size=4. We have also included events to capture the response to the three major US summer holidays (Memorial Day, Fourth of July and Labor Day). Notice how smooth the forecasts are and how they go down in the winter and up in the summer without all of the unexplainable random deviations.

In expert selection mode, Forecast Pro XE will automatically build seasonally simplified models when they are appropriate. In Forecast Pro Unlimited and Forecast Pro TRAC, if you wish expert selection mode to automatically build seasonally simplified models when they are appropriate, you must turn the Exclude seasonal simplification option off (this option is found on the Advanced Controls tab of the Options dialog box). The automatic selection algorithm uses out-of-sample performance to select between standard smoothing models and the seasonally simplified forms. The test is time consuming, which is why the default in expert selection mode in Forecast Pro Unlimited and Forecast Pro TRAC is to not consider seasonally simplified models.

About the author:
EricEric Stellwagen is the co-founder of Business Forecast Systems, Inc. and the co-author of the Forecast Pro software product line. With more than 29 years of expertise, he is widely recognized as a leader in the field of business forecasting. He has consulted extensively with many leading firms—including Coca-Cola, Procter & Gamble, Merck, Blue Cross Blue Shield, Nabisco, Owens-Corning and Verizon—to help them address their forecasting challenges. Eric has presented workshops for a variety of organizations including APICS, the International Institute of Forecasters (IIF), the Institute of Business Forecasting (IBF), the Institute for Operations Research and the Management Sciences (INFORMS), and the University of Tennessee. He is currently serving on the board of directors of the IIF and the practitioner advisory board of Foresight: The International Journal of Applied Forecasting.