A system of time-varying models for predictive regressions

This paper proposes a system of time-varying models for predictive regressions, where a time-varying autoregressive (TV-AR) process is introduced to model the dynamics of the predictors and a linear control function approach is used to improve the estimation efficiency. We employ a profile likelihood estimation method to estimate both constant and time-varying coefficients and propose a hypothesis test to examine the parameter stability. We establish the asymptotic properties of the proposed estimators and test statistics accordingly. Monte Carlo simulations show that the proposed methods work well in finite samples. Empirically, the TV-AR process effectively approximates the time-series behavior of a broad set of potential predictors. Furthermore, we reject the stability assumption of predictive models for more than half of these predictors. Finally, the linear projection method not only improves estimator efficiency but also enhances out-of-sample forecasting performance, leading to significant utility gains in forecasting experiments.