Testing for causality in variance using multivariate GARCH models

Abstract

Tests of causality in variance in multiple time serieshave been proposed recently, based on residuals of estimatedunivariate models. Although such tests are applied frequentlylittle is known about their power properties. In this paper weshow that a convenient alternative to residual based testing is tospecify a multivariate volatility model, such as multivariateGARCH (or BEKK), and construct a Wald test on noncausality invariance. We compare both approaches to testing causality invariance in terms of asymptotic and finite sample properties. TheWald test is shown to have superior power properties under asequence of local alternatives. Furthermore, we show by simulationthat the Wald test is quite robust to misspecification of theorder of the BEKK model, but that empirical power decreasessubstantially when asymmetries in volatility are ignored.causality;local power;multivariate volatility