Damped Seasonality Factors: Introduction

Previous research has shown that seasonal factors provide one of the most important ways to improve forecast accuracy. For example, in forecasts over an 18-month horizon for 68 monthly economic series from the MCompetition, Makridakis et al. (1984, Table 14) found that seasonal adjustments reduced the MAPE from 23.0 to 17.7 percent, an error reduction of 23%. On the other hand, research has also shown that seasonal factors sometimes increase forecast errors (e.g., Nelson, 1972). So, when forecasting with a data series measured in intervals that represent part of a year, should one use seasonal factors or not? Statistical tests have been devised to answer this question, and they have been quite useful. However, some people might say that the question is not fair. Why does it have to be either/or? Shouldn’t the question be "to what extent should seasonal factors be used for a given series?" Comments Postprint version. Published in International Journal of Forecasting, Volume 20, Issue 4, June 2004, pages 525-527. Publisher URL: http://dx.doi.org/10.1016/j.ijforecast.2004.03.001 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/marketing_papers/53 1 Damped Seasonality Factors: Introduction Forthcoming, International Journal of Forecasting J. Scott Armstrong The Wharton School University of Pennsylvania, Philadelphia, PA [email protected] Previous research has shown that seasonal factors provide one of the most important ways to improve forecast accuracy. For example, in forecasts over an 18-month horizon for 68 monthly economic series from the M-Competition, Makridakis et al. (1984, Table 14) found that seasonal adjustments reduced the MAPE from 23.0 to 17.7 percent, an error reduction of 23%. On the other hand, research has also shown that seasonal factors sometimes increase forecast errors (e.g., Nelson, 1972). So, when forecasting with a data series measured in intervals that represent part of a year, should one use seasonal factors or not? Statistical tests have been devised to answer this question, and they have been quite useful. However, some people might say that the question is not fair. Why does it have to be either/or? Shouldn’t the question be “to what extent should seasonal factors be used for a given series?” Damping as a Basic Strategy for Forecasting One solution to “to what extent” relies on damping. Basically, damping says that the forecaster is more conservative as uncertainty increases. In 1978, in summarizing research by others, I concluded that trends should be damped (Armstrong 1978, p.153). As nearly as I can tell, only two people took action: Gardner and Mackenzie (1985) provided convincing evidence that damping improved accuracy. Just as important, they provided an operational procedure. Their effort led to one of the more important advances in extrapolation. Again drawing on the research of others, I concluded in Armstrong (1978, 148-150) that seasonal factors should be damped. Here also only two people listened. Miller and Williams (2003, 2004) have obtained convincing evidence that damped seasonal factors improve forecast accuracy. They have also developed an operational procedure for doing this. Is the Miller-Williams’ procedure optimal? Along with the panelists (including Miller and Williams), I am skeptical that it is. However, I expect that their statistical procedures for damping seasonality will prove to be nearly optimal. Their two papers provide evidence from simulations and from analyses of monthly series. For the real data, damping improved accuracy in about 60% of the series, with about a 4% error reduction.