Wild bootstrap Ljung-Box test for cross correlations of multivariate time series

•Ljung-Box test for the cross correlation in mean of multivariate time series with conditional heteroscedasticity tends to suffer from severe size distortions.•Wild bootstrap-based Ljung-Box test for cross correlations in mean of multivariate time series is proposed.•According to the simulation study, wild bootstrap-based Ljung-Box test shows no size distortion and comparable powers in the presence of conditional heteroscedasticity.

In the literature, the conventional Ljung-Box test for financial time series with ARCH effect (also known as conditional heteroscedasticity) is well-known to suffer from severe size distortions. The objective of this paper is to develop a wild bootstrap-based Ljung-Box test for cross correlations in mean of multivariate time series. According to our simulation study, the wild bootstrap-based Ljung-Box test succeeds to achieve correct sizes and comparable powers in the presence of ARCH effect.