New Methods for Inference in Long-Run Predictive Regressions

Abstract

I develop new asymptotic results for long-horizon regressions with overlapping observations. I show that rather than using auto-correlation robust standard errors, the standard t-statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data. Further, when the regressors are persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and similar corrections and test procedures as those proposed for the short-run case should also be used in the long-run. In addition, I show that under an alternative of predictability, long-horizon estimators have a slower rate of convergence than short-run estimators and their limiting distributions are non-standard and fundamentally different from those under the null hypothesis. These asymptotic results are supported by simulation evidence and suggest that under standard econometric specifications, short-run inference is generally preferable to long-run inference. The theoretical results are illustrated with an application to long-run stock-return predictability.