Time series forecasting : advances on Theta method

Abstract

Accurate and robust forecasting methods for univariate time series are critical as the historical data can be used in the strategic planning of such future operations as buying and selling to ensure product inventory and meet market demands. In this context, several competitions for time series forecasting have been organized, with the M3-Competition as the largest. As the winner of M3-Competition, the Theta method has attracted attention from researchers for its predictive performance and simplicity. The Theta method is a combination of other methods, which proposes the decomposition of the deseasonalized time series into two other time series called "theta lines". The first completely removes the curvatures of the data, thus accurately estimating the long-term trend. The second doubles the curvatures to better approximate short-term behavior. Several issues have been raised about the Theta method, even by its originators. They include the number of theta lines, their parameters, weights to combine them, and construction of prediction intervals, among others. This doctorate thesis resolves part of these issues. We derive optimal weights for combine the theta lines, this result is used to derive statistical models which generalizes /approximate the standard Theta method. The statistical methodology is considering for parameter estimation and for compute the prediction intervals. The optimal weights are also used to propose new methods that hold two or more theta lines. Part of proposed methodology is implemented in a package for R-programming language. In an empirical investigation using the M3-Competition data set with more than 3000 time series, the proposed methods/models demonstrated significant accuracy. The study’s primary approach, the Dynamic Optimised Theta Model, outperformed all benchmarks methods, constituting, in all likelihood, the highest-performing method for this data set available in the literature.