Robust inference for predictability in smooth transition predictive regressions

This article provides a novel test for predictability within a nonlinear smooth transition predictive regression (STPR) model where inference is complicated due not only to the presence of persistent, local to unit root, predictors, and endogeneity but also the presence of unidentified parameters under the null of no predictability. In order to circumvent the unidentified parameters problem, t− statistic for the predictor in the STPR model is optimized over the Cartesian product of the spaces for the transition and threshold parameters; and to address the difficulties due to persistent and endogenous predictors, the instrumental variable (IVX) method originally developed in the linear cointegration testing framework is adopted within the STPR model. Limit distribution of this statistic (i.e., sup−tIVX test) is shown to be nuisance parameter-free and robust to the local to unit root and endogenous regressors. Simulations show that sup−tIVX has good size and power properties. An application to stock return predictability reveals presence of asymmetric regime-dependence and variability in the strength and size of predictability across asset-related (e.g., dividend/price ratio) vs. other (e.g., default yield spread) predictors.