The theta model: a decomposition approach to forecasting

This paper presents a new univariate forecasting method. The method is base d on the concept of modifying the local curvature of the time-series throug h a coefficient 'Theta' (the Greek letter theta), that is applied directly to the second differences of the data. The resulting series that are create d maintain the mean and the slope of the original data but not their curvat ures. These new time series are named Theta-lines. Their primary qualitativ e characteristic is the improvement of the approximation of the long-term b ehavior of the data or the augmentation of the short-term features, dependi ng on the value of the Theta coefficient. The proposed method decomposes th e original time series into two or more different Theta-lines. These are ex trapolated separately and the subsequent forecasts are combined. The simple combination of two Theta-lines, the Theta = 0 (straight line) and Theta = 2 (double local curves) was adopted in order to produce forecasts for the 3 003 series of the M3 competition. The method performed well, particularly f or monthly series and for microeconomic data. (C) 2000 Elsevier Science B.V . All rights reserved.