Equity Premium Prediction with Structural Breaks: A Two-Stage Forecast Combination Approach

Abstract

This paper introduces a two-stage out-of-sample predictive model averaging approach to forecasting the U.S. market equity premium. In the first stage, we combine the break and stable specifications for each candidate model utilizing schemes such as Mallows weights to account for the presence of structural breaks. Next, we combine all previously averaged models by equal weights to address the issue of model uncertainty. Our empirical results show that the double-averaged model can deliver superior statistical and economic gains relative to not only the historical average but also the simple forecast combination when forecasting the equity premium. Moreover, our approach provides an explicit theory-based linkage between forecast combination and structural breaks which distinguishes this study from other closely related works.In response to the findings reported in Goyal and Welch (2008), recent developments in the literature of forecasting equity returns show that the predictive power of various predictors can be uncovered or restored once an appropriate estimation methodology other than OLS is employed. Based on the general framework considered in Goyal and Welch (2008), Rapach, Strauss, and Zhou (2010) demonstrate that forecast combination could consistently improve upon the historical mean benchmark over time in terms of both statistical and economic gains. Additionally, they argue that, due to the uncertainty regarding model selection and parameter instability, the benefits of forecast combination come from taking advantage of all available information and its linkage to the real economy. However, it is not clear how the weighting methods combining models considered in Rapach et al. (2010) are explicitly linked with structural breaks. Specifically, despite the empirical evidence of instability documented in works such as Rapach and Wohar (2006), Rapach et al. (2010) do not consider any candidate model which allows for breaks when combining models, resulting in difficulty in interpreting the empirical results linking the success of forecast combination with structural breaks.Our main contribution to the literature is to introduce a two-stage forecast combination methodology which improves upon the simple model averaging and can be easily implemented in empirical works. Our approach explicitly accounts for the possible presence of structural breaks beside the uncertainty on model selection,