A System of Time-Varying Models for Predictive Regressions

This paper proposes a system of semiparametric time-varying models for predictive regressions, where a locally stationary process in the form of time-varying autoregression is introduced to model varying-persistent predictors, and parameter instability and embedded endogeneity have also been taken into account simultaneously. We employ a semiparametric profile likelihood approach to
estimate both constant parameters and time-varying functional coefficients, and we further establish the asymptotic theory of the estimators in the system. Monte Carlo simulations show that the proposed estimation method works very well in finite samples. Empirically, we find that the popular predictors considered in the literature are well approximated by a time-varying first-order autoregressive process, those predictors generally contain significant and time-varying predictive content of future equity premium, and taking embedded endogeneity into account helps to identify the existence of return predictability.