Using Evolutionary Spectra to Forecast Time Series

In this paper, an adaptive smoothing forecasting approach based on evolutionary spectra as developed by Rao and Shapiro (1970) is applied to the 3003 time series of various types and lengths used in the M3-Competition (Makridakis and Hibon, 2000). Comparisons of out-of-sample forecasts are made with other methods used in the M3-Competition via the symmetric mean absolute percentage error (SMAPE). It will be seen that this method does appear to perform very well when applied specifically to yearly, quarterly and monthly macro time series and to yearly and monthly demographic time series used in the competition.