| Abstract: | This article proposes a new technique for estimating trend and multiplicative seasonality in time series data. The technique is computationally quite straightforward and gives better forecasts (in a sense described below) than other commonly used methods. Like many other methods, the one presented here is basically a decomposition technique, that is, it attempts to isolate and estimate the several subcomponents in the time series. It draws primarily on regression analysis for its power and has some of the computational advantages of exponential smoothing. In particular, old estimates of base, trend, and seasonality may be smoothed with new data as they occur. The basic technique was developed originally as a way to generate initial parameter values for a Winters exponential smoothing model [4], but it proved to be a useful forecasting method in itself.The objective in all decomposition methods is to separate somehow the effects of trend and seasonality in the data, so that the two may be estimated independently. When seasonality is modeled with an additive form (Datum = Base + Trend + Seasonal Factor), techniques such as regression analysis with dummy variables or ratio-to-moving-average techniques accomplish this task well. It is more common, however, to model seasonality as a multiplicative form (as in the Winters model, for example, where Datum = [Base + Trend] * Seasonal Factor). In this case, it can be shown that neither of the techniques above achieves a proper separation of the trend and seasonal effects, and in some instances may give highly misleading results. The technique described in this article attempts to deal properly with multiplicative seasonality, while remaining computationally tractable.The technique is built on a set of simple regression models, one for each period in the seasonal cycle. These models are used to estimate individual seasonal effects and then pooled to estimate the base and trend. As new data occur, they are smoothed into the least-squares formulas with computations that are quite similar to those used in ordinary exponential smoothing. Thus, the full least-squares computations are done only once, when the forecasting process is first initiated. Although the technique is demonstrated here under the assumption that trend is linear, the trend may, in fact, assume any form for which the curve-fitting tools are available (exponential, polynomial, etc.).The method has proved to be easy to program and execute, and computational experience has been quite favorable. It is faster than the RTMA method or regression with dummy variables (which requires a multiple regression routine), and it is competitive with, although a bit slower than, ordinary triple exponential smoothing. |
