Application of bootstrap methods in investigation of size of the Granger causality test for integrated VAR systems

This paper examines the size performance of Toda-Yamamoto test for Granger causality in case of trivariate integrated-cointegrated VAR systems and relatively small sample size. The standard asymptotic distribution theory and the residual-based bootstrap approach are applied. A variety of types of distribution of error term is considered. The impact of misspecification of initial parameters as well as the influence of increase of sample size and number of bootstrap replications on size performance of Toda-Yamamoto test statistics is also examined. The results of conducted simulation study confirm that standard asymptotic distribution theory may often cause significant over-rejection. Application of bootstrap methods usually leads to improvement of size performance of Toda-Yamamoto test. However, in some cases considered bootstrap method also leads to serious size distortion and performs worse than the traditional approach based on distribution.