Testing predictive regression models with nonstationary regressors

Due to nonstationary (nearly integrated or integrated) regressors and the embedded endogeneity, a linear predictive regression model produces biased coefficient estimates, which consequentially leads to the conventional t-test to over-reject the misspecification test. In this paper, our aim is to find an appropriate and easily implemented method for estimating and testing coefficients in predictive regression models. We apply a projection method to remove the embedded endogeneity and then adopt a two-step estimation procedure to manage both highly persistent and nonstationary predictors. The asymptotic distributions of these estimates are established under α-mixing innovations, and different convergence rates among the coefficients are derived for different persistent degrees. We also consider the model with the regressor having a drift in its autoregressive model and show that the asymptotic properties for the estimated coefficients are totally different from the case without drift. To conduct a misspecification test, we rely on the deduced asymptotic distributions and use the Monte Carlo simulation to find the appropriate critical values. A Monte Carlo experiment is then conducted to illustrate the finite sample performance of our proposed estimator and test statistics. Finally, an empirical example is examined to demonstrate the proposed estimation and testing method.