Tests of causality in variance in multiple time series
have been proposed recently, based on residuals of estimated
univariate models. Although such tests are applied frequently
little is known about their power properties. In this paper we
show that a convenient alternative to residual based testing is to
specify a multivariate volatility model, such as multivariate
GARCH (or BEKK), and construct a Wald test on noncausality in
variance. We compare both approaches to testing causality in
variance in terms of asymptotic and finite sample properties. The
Wald test is shown to have superior power properties under a
sequence of local alternatives. Furthermore, we show by simulation
that the Wald test is quite robust to misspecification of the
order of the BEKK model, but that empirical power decreases
substantially when asymmetries in volatility are ignored