Predictive regression with p-lags and order-q autoregressive predictors

This paper considers predictive regressions, where yt is predicted by all p lags of xt, here with xt being autoregressive of order q, PR(p,q). The literature considers model properties in the cases where p=q. We demonstrate that the current augmented regression method can still reduce the bias in predictive coefficients, but its efficiency depends on correctly specifying both p and q. We propose an estimation framework for the predictive regression, PR(p,q), with a data-driven auto-selection of p and q to achieve the best bias reduction in predictive coefficients. The corresponding hypothesis testing procedure is also derived. The efficiency of the proposed method is demonstrated with simulations. Empirical applications to equity premium prediction illustrate the substantial difference between the estimates of our method and those obtained by the common predictive regressions with p=q