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

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 infinity but at a slower rate than the sample size, wehave the VAR order grow at the same rate, as a fixed fraction of the sample size. Under thisfixed-smoothing asymptotic specification, the associated Wald statistic remains asymptot-ically pivotal. On the basis of this asymptotics, we introduce a new and easy-to-use F test that employs a Önite sample corrected Wald statistic and uses critical values from an Fdistribution. 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 Ftest with the empirical order selection is much more accuratein size than the conventional chi-square test