On Robust Inference in Time Series Regression

Abstract

Least squares regression with heteroskedasticity consistent standard errors ("OLS-HC regression") has proved very useful in cross section environments. However, several major difficulties, which are generally overlooked, must be confronted when transferring the HC technology to time series environments via heteroskedasticity and autocorrelation consistent standard errors ("OLS-HAC regression"). First, in plausible time-series environments, OLS parameter estimates can be inconsistent, so that OLS-HAC inference fails even asymptotically. Second, most economic time series have autocorrelation, which renders OLS parameter estimates inefficient. Third, autocorrelation similarly renders conditional predictions based on OLS parameter estimates inefficient. Finally, the structure of popular HAC covariance matrix estimators is ill-suited for capturing the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in HAC-based hypothesis testing, in all but the largest samples. We show that all four problems are largely avoided by the use of a simple and easily-implemented dynamic regression procedure, which we call DURBIN. We demonstrate the advantages of DURBIN with detailed simulations covering a range of practical issues.