Theta Model Forecasts for Financial Time Series: A Case Study in the S&P500

The Theta model created a lot of interest in academic circles due to its surprisingly good performance in the M3 forecasting competition. However, this interest was not followed up by other studies, with the exception of Hyndman and Billah in 2003. In addition, the Theta model performance has not been tested on a large dataset of non-demand forecasting series, nor its properties have been examined analytically for time series that are found in finance and economics. The present study presents some empirical results on the application of the Theta model for forecasting the evolution of the S&P500 index, both as an examination of its relative performance against the standard benchmarks, and as a motivation for further theoretical work. We use weekly data over a long period of 20 years and the Theta model is used alongside the benchmark models and rolling-origin forecasts are generated. The results are interesting since they show that the Theta model has performance that is either on par or better than the benchmarks.