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abstract

Accurate and robust forecasting methods for univariate time series are very important when the objective is to produce estimates for large numbers of time series. In this context, the Theta method’s performance in the M3-Competition caught researchers’ attention. The Theta method, as implemented in the monthly subset of the M3-Competition, decomposes the seasonally adjusted data into two ‘‘theta lines’’. The first theta line removes the curvature of the data in order to estimate the long-term trend component. The second theta line doubles the local curvatures of the series so as to approximate the shortterm behaviour. We provide generalisations of the Theta method. The proposed Dynamic Optimised Theta Model is a state space model that selects the best short-term theta line optimally and revises the long-term theta line dynamically. The superior performance of this model is demonstrated through an empirical application. We relate special cases of this model to state space models for simple exponential smoothing with a drift. © 2016 The Author(s). Published by Elsevier B.V. on behalf of International Institute of Forecasters.

5. Concluding remarks

In this paper, we have proposed a generalisation of the Theta method, namely the dynamic optimised Theta model. The DOTM selects the theta line to be used for the extrapolation of the short-term component of the series optimally, and also revises the At and Bt in the longterm component at each time period t. In addition, the proposed model is provided under a state space approach, which allows already consolidated statistical tools to be used for parameter estimation. The newly proposed model was contrasted with the original Theta method and other variants such as the SES-d model, both theoretically and empirically.