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Forecasting 101: Going Beyond Automatic Forecasting
Part 3: Improving Your Forecasting with Top-down Models

This installment of Forecasting 101 presents the third of three articles about going beyond automatic forecasting. The first article presented an overview of automatic time series approaches, examining how they work, the pros and cons of using them, and situations where they should not be utilized. The second article described the evolution of a successful forecasting process, noting that it often involves a progression from ad hoc spreadsheets to automatic time series approaches and finally to customized approaches being applied to the subset of the items where they add value. The second article described one such customized approach—event models—an advanced forecasting method which will often outperform automatic time series approaches for data where special events such as promotions, strikes, moveable holidays, etc. have occurred during the historic demand period.

In this article we will look at another common customized approach—top-down modeling. Top-down approaches leverage structure that exists in higher-level aggregate data to improve forecasts at lower levels of the forecasting hierarchy.

What is a top-down forecast?
Most organizations deal with multiple levels of aggregation and require consistent forecasts at all levels. For instance a beverage company might need a forecast for total sales, as well as a forecast for each brand, each customer segment, each container type and each SKU.

When preparing forecasts for hierarchical data, you must decide upon a reconciliation strategy (i.e., you must decide how to enforce that the forecasts are consistent across levels). One approach is to apply statistical forecasting methods directly to the lowest-level demand histories and construct all group-level forecasts by summing the lower-level forecasts—this is known as a bottom-up forecast. An alternative approach is to use statistical forecasting methods on more aggregated data and then to apply an allocation scheme to generate the lower-level forecasts—this is known as a top-down forecast.

Let’s illustrate these approaches with a very simple example.

   
Model-Based
 
Bottom-Up
 
Top-Down
6 packs  
70
 
70
 
84
12 packs  
30
 
30
 
36
Cans  
120
 
100
 
120

The column labeled Model-Based contains the forecast that would be created by applying a statistical forecasting method directly to the given data set. Thus in our example, if you forecasted the demand for 6 packs directly the forecast would equal 70, if you forecasted the demand for 12 packs directly the forecast would equal 30 and if you forecasted the demand for total cans directly the forecast would equal 120. Notice that forecast for Cans does not equal the sum of the forecast for 6 packs and the forecast for 12 packs. When the three data sets are forecasted independently using their own histories, there is no statistical mechanism that forces them to reconcile and they are extremely unlikely to do so. At times, the model-based forecast for the group can be quite different than the sum of the component series’ model-based forecasts.

Notice that in the bottom-up approach the model-based forecasts are used for the item-level data (6 packs and 12 packs) and the group-level forecast (Cans) is calculated as their sum. In the top-down approach the model-based forecast is used for the group-level and the item-level forecasts are calculated by adjusting their model-based forecasts proportionally so that they sum to the group-level forecast.

An alternative top-down approach is to not forecast the item-level data at all and just disaggregate the group-level forecast by applying proportionality factors. This method would be appropriate when the proportions are constant and known (e.g., disaggregating shoe sales using a size chart or a finished good using a bill of materials).

When do top-down approaches improve the forecasts?
The decision to use a top-down or a bottom-up approach often hinges upon two important issues.

1. Are the lower level units likely to require distinct statistical models?

This would be the case if the market forces that shape sales at the lower level are different. Different markets, different advertising and promotion, and different distribution all favor creation of distinct model-based forecasts. If apples and oranges have distinctly different markets, then you will probably do better to forecast them separately.

If not, then there is often a distinct advantage to forecasting top down from the aggregated “fruit.” If the lower-level data are statistically similar, forecasting at a group level will generally result in a more accurate forecast because:

    A. a higher volume of data is available.

    B. there is less “noise” (random variation) in the aggregated data that could skew the forecast.

    C. the aggregated data will often exhibit a more pronounced structure, making patterns easier to recognize and forecast.

2. Is there sufficient statistical information in the lower level historic sales to construct a model based only on those sales?

Many organizations that need to generate low-level forecasts discover that at the lowest levels there simply is not enough structure to generate meaningful statistical forecasts directly from the low-level data. In these cases there is little choice but to generate the lowest-level forecasts not with statistical models, but rather by using some type of top-down allocation scheme.

Let’s illustrate this with an example.

Figure 1

Figure 2

Figure 1 shows monthly sales for a brand of cough syrup. Figure 2 shows monthly sales for a specific SKU. The company assigns a unique SKU number to each flavor-by-bottle-size combination that it produces.

Consider the two graphs. Notice that at the brand level, there is more structure to the data. The seasonal pattern is readily apparent and there is less noise. More than three years of demand history is available at the brand level, while only 10 months of history exists for the recently introduced SKU.

In this example, the lack of history at the SKU level doesn’t allow you to build a seasonal forecasting model directly from the data. Thus, since cough syrup is clearly a seasonal product, a bottom-up approach will yield very poor forecasts. On the other hand, a top-down approach allows you to capture the seasonal structure that exists at the group level and introduce it to the SKU-level forecasts via the top-down adjustments.

Summary
Most organizations find that using automated time series approaches—such as those implemented in Forecast Pro—work quite well for the vast majority of their items and offer substantial advantages over ad hoc forecasting with spreadsheets. In this series of articles, we have discussed the pros and cons of automatic time series approaches and also explored event modeling and top-down forecasting—two alternative forecasting approaches that often improve forecast accuracy for the subset of your items where automatic time series models do not perform well.

About the author:
Eric Stellwagen is Vice President and co-founder of Business Forecast Systems, Inc. (BFS) and co-author of the Forecast Pro software product line. He consults widely in the area of practical business forecasting—spending 20-30 days a year presenting workshops on the subject—and frequently addresses professional groups such as the University of Tennessee’s Sales Forecasting Management Forum, APICS and the Institute for Business Forecasting. Recognized as a leading expert in the field, he has worked with numerous firms including Coca-Cola, Procter & Gamble, Merck, Blue Cross Blue Shield, Nabisco, Owens-Corning and Verizon. He is also currently serving on the board of directors of the International Institute of Forecasters (IIF).

 

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