A test for volatility spillover with application to exchange rates

This paper proposes a class of asymptotic N(0,1) tests for volatility spillover between two time series that exhibit conditional heteroskedasticity and may have infinite unconditional variances. The tests are based on a weighted sum of squared sample cross-correlations between two squared standardized residuals. We allow to use all the sample cross-correlations, and introduce a flexible weighting scheme for the sample cross-correlation at each lag. Cheung and Ng (1996) test and Granger (1969)-type regression-based test can be viewed as uniform weighting because they give equal weighting to each lag. Non-uniform weighting often gives better power than uniform weighting, as is illustrated in a simulation study. We apply the new tests to study Granger-causalities between two weekly nominal U.S. dollar exchange rates—Deutschemark and Japanese yen. It is found that for causality in mean, there exists only simultaneous interaction between the two exchange rates. For causality in variance, there also exists strong simultaneous interaction between them. Moreover, a change in past Deutschemark volatility Granger-causes a change in current Japanese yen volatility, but a change in past Japanese yen volatility does not Granger-cause a change in current Deutschemark volatility.