  Knowing the error distribution is important in many multivariate time series
applications. To alleviate the risk of error distribution mis-specification,
testing methodologies are needed to detect whether the chosen error
distribution is correct. However, the majority of the existing tests only deal
with the multivariate normal distribution for some special multivariate time
series models, and they thus can not be used to testing for the often observed
heavy-tailed and skewed error distributions in applications. In this paper, we
construct a new consistent test for general multivariate time series models,
based on the kernelized Stein discrepancy. To account for the estimation
uncertainty and unobserved initial values, a bootstrap method is provided to
calculate the critical values. Our new test is easy-to-implement for a large
scope of multivariate error distributions, and its importance is illustrated by
simulated and real data.
