Choice of Time-Series Forecasting Method Using Discriminant Scores

A lot of research has been done on comparing the forecasting accuracy of different univariate time series forecasting methods. The biggest such study, using empirical data, was undertaken by Makridakis et al. (1982). The evidence from such comparative studies indicate that there is not one "best" method for all kinds of data. Furthermore, there also seems to be evidence to suggest that the simpler methods, such as exponential smoothing, often perform as well as or even better than the more complex methods. This is particularly true for short term forecasting. Unfortunately, there has been limited success in identifying the factors that contribute to the relative advantage of one method over another. Consequently a practitioner is still faced with the problem of objectively choosing one out of several methods available to use in forecasting a given time series. In this paper we address this problem by considering certain characteristics of a time series in order to calculate its discriminant score. This score is then used to calculate the probability of a particular method being "best" in forecasting that series. Three forecasting methods, simple exponential smoothing, Holt-Winters method and basic structural time series model using the STAMP package, are considered. Quarterly time series from Makridakis et al. (1982) "M-Competition" are used as data.