A New Asymptotic Theory for Vector Autoregressive Long-Run Variance Estimation and Autocorrelation Robust Testing

Abstract

We develop a new asymptotic theory for autocorrelation robust tests using a vector autoregressive (VAR) covariance matrix estimator. In contrast to the conventional asymptotics where the VAR order goes to in…nity but at a slower rate than the sample size, we have the VAR order grow at the same rate, as a …xed fraction of the sample size. Under this …xed-smoothing asymptotic speci…cation, the associated Wald statistic remains asymptotically pivotal. On the basis of this asymptotics, we introduce a new and easy-to-use F test that employs a …nite sample corrected Wald statistic and uses critical values from an F distribution. We also propose an empirical VAR order selection rule that exploits the connection between VAR variance estimation and kernel variance estimation. Simulations show that the new VAR F test with the empirical order selection is much more accurate in size than the conventional chi-square test.