Standard Errors for Predictive Regression with Overlapping Observations

Inference of predictive regression over multiple horizons is challenging because of over- lapping observations. We show that the size of the test based on the popular Hodrick standard errors can approach one if the horizon grows at a faster rate than the rotated norm of short-run predictability slopes approaches zero. We propose a modification based on the martingale representation of the partial-sum process of the score. The new test is asymptotically equivalent to Hodrick's under the condition of constant expected returns, and is robust to this condition. Simulations and empirical applications demonstrate the findings and the remarkable finite-sample performance of the new method