Non-Linear Predictability in Stock and Bond Returns: When and Where is it Exploitable?

Abstract

We systematically examine the comparative predictive performance of a number of linear and non-linear models for stock and bond returns in the G7 countries. Besides Markov switching, threshold autoregressive (TAR), and smooth transition autoregressive (STAR) regime switching models, we also estimate univariate models in which conditional heteroskedasticity is captured by a GARCH and in which predicted volatilities appear in the conditional mean function. Although we fail to find a consistent winner/out performer across all countries and markets, it turns out that capturing non-linear effects may be key to improve forecasting. U.S. and U.K. asset return data are special in the sense that good predictive performance seems to require that non-linear dynamics be modeled, especially using a Markov switching framework. Although occasionally stock and bond return forecasts for other G7 countries also appear to benefit from non-linear modeling (especially of TAR and STAR type), data from France, Germany, and Italy imply that the best predictive model is often one of the simple benchmarks, such as the random walk and univariate auto-regressions. U.S. and U.K. markets also provide the only data for which we find statistically significant differences between forecasting models. Results appear to be remarkably stable over time, robust to changes in the loss function used in statistical evaluations as well as to the methodology employed to perform pairwise comparisons.