Finite-sample simulation-based inference in VAR models with application to Granger causality testing

Tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, we propose a general simulation-based technique that allows one to control completely test levels in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour, 2005. Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics in econometrics. Journal of Econometrics, forthcoming] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to a VAR model of the U.S. economy.