Higher Order Approximations for Wald Statistics in Cointegrating Regressions

Asymptotic expansions are developed for Wald test statistics in cointegrating regression models. These expansions provide an opportunity to reduce size distortion in testing by suitable bandwidth selection, and automated rules for doing so are calculated. Band spectral regression methods and tests are also considered. In such cases, it is shown how the effects of nonstationarity that dominate low frequency limit behaviour also carry over to high frequency asymptotics, with consequential effects on bandwidth rules.