Revisiting Top-Down versus Bottom-Up Forecasting

Abstract

Top-down approach achieves a betterforecastat the aggregate level and bottom-up approach, at the lowest level... a top-down approach assumes that one seasnonal pattern fits all, that is, the seasonal pattern both at the aggregate and disaggregate levels are the same, which is often not the case ... a hybrid approach which combines both may be the solution. What is the best approach to sales forecasting? Is it a top-down approach, where national brand forecasts are proportioned down to individual product items per location forecasts? Or is it a bottom-up approach, where item per location forecasts are aggregated up to create a national brand forecast? Various opinions support either approach. Proponents of top-down forecasting favor smoothing lower level data by aggregating it so that one can develop a better fitting model (the toplevel model will reflect a better R2 value than lower level models). It is also felt that top-down models often reflect better accuracy for top-level forecasting. The problem is top-down models typically do a poor job of forecasting at lower forecast levels (e.g., ' at the item per location level). The reason: aggregated data at the toplevel is an artificial representation of the true nature of the business because such data does not typically reflect sales low level peaks and valleys, which are canceled by aggregation. Proponents of bottom-up forecasting point to the fact that one can achieve a better mean absolute percent error (MAPE) value at the lower level (see Gordon, Morris, and Dangerfield 1997). This is due in part to the fact that the lower level models reflect the actual nature of the business. A bias also has been documented in regression coefficients when aggregated data is used (see Blattberg and Neslin 1990). While this supports a bottom-up approach, bottom-up forecasting often has very poor accuracy at higher forecast levels. This may be a result of forecast error at intermediate (middle) levels accumulating as data moves up to higher levels. Naturally, choosing whether to use a top-down or bottom-up forecasting approach should depend on the objective driving why one forecasts. If the company uses forecasts to develop strategic plans and budgets, then top-down forecasting would be preferable. Conversely, if production and distribution schedules (tactical side of the business) are driven by forecasts, then bottom-up forecasting would probably be a preferred choice. There are, of course, many companies that generate one forecast by reconciling topdown and bottom-up forecasts. Which approach should be used? Based on research conducted with a major consumer products company, a hybrid approach may be preferable. That is, a top-down model can be created and forecasts proportioned down to lower forecast levels by lower level models (lower level analyses). The purpose of this paper is to overview such an approach. UNDERLYING ISSUES The basic problem with top level and low level data stems from the issue of variability. As shown in Figure 1, aggregated data at the highest level is smoother than lower level data and corresponds to lower percent differences about the means of individual time series at respective forecast levels. Thus, aggregation reduces variability. Interestingly, research indicates that top-level data reflects more randomness than lower level data. That is, top-level data, while smoothed, exhibits small random fluctuations. One should therefore realize that aggregation of sales data reduces data swings (reduces variability), but introduces random fluctuations (increases random-ness) (see Kahn 1998). This explains why top-down and bottom-up approaches have difficulty forecasting at the opposite end of the spectrum. Top-down forecasts have difficulty with lower level forecasting because the model is based on an artificial, more random data set. But forecasts based on top-level data achieve a better model fit at higher levels because there is less relative variability in the data. …