On Robust Inference in Time Series Regression

Least squares regression with heteroskedasticity and autocorrelation consistent (HAC) standard errors has proved very useful in cross section environments. However, several major di?culties, which are generally overlooked, must be confronted when transferring the HAC estimation technology to time series environments. First, most economic time series have strong autocorrelation, which renders HAC regression parameter estimates highly inef?cient. Second, strong autocorrelation similarly renders HAC conditional predictions highly ine?cient. Finally, the structure of most popular HAC estimators is ill-suited to capture the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in hypothesis testing, in all but the largest sample sizes. We show that all three problems are largely avoided by the use of a simple dynamic regression (DynReg), which is easily implemented and also avoids possible problems concerning strong exogeneity. We demonstrate the advantages of DynReg with detailed simulations covering a range of practical issues.