Non-linear predictability in stock and bond returns: when and where is it exploitable?

We systematically examine the comparative predictive performance of a number of alternative 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 (predictive) regression models, we also estimate univariate models in which conditional heteroskedasticity is captured through GARCH, TARCH and EGARCH models and ARCH-in mean effects appear in the conditional mean. Although we fail to find a consistent winner/out-performer across all countries and asset markets, it turns out that capturing non-linear effects is of extreme importance to improve forecasting performance. U.S. and U.K. asset return data are “special” in the sense that good predictive performance seems to loudly ask for models that capture non linear dynamics, especially of the Markov switching type. Although occasionally also stock and bond return forecasts for other G7 countries appear to benefit from non-linear modeling (especially of TAR and STAR type), data from France, Germany, and Italy express interesting predictive results on the basis of simpler benchmarks. U.S. and U.K. data are also the only two data sets in which we find statistically significant differences between forecasting models. Results appear to be remarkably stable over time, and robust to the specification of the loss function used in statistical evaluations as well as to the methodology employed to perform pairwise comparisons.