On the Properties of Regression Tests of Asset Return Predictability

This paper investigates, both in finite samples and asymptotically, statistical inference on predictive regressions where time series are generated by present value models of asset prices. We show that regression-based tests, including robust tests such as robust conditional test and Q-test, are inconsistent and thus suffer from lack of power in local-to-unity models for the regressor persistence. The main reason is that the near-integrated regressor from the present value model slows down the convergence rates of the estimates, an effect which is masked in predictive regressions analysis with exogenous constant covariance of innovations. We illustrate these properties in a simulation study and analyze the predictability of several stock returns series.