Statistical tests for realized multivariate volatility models

We investigate statistical tests for multivariate realized volatility models which are estimated using realized covariance matrices computed from intraperiod (high-frequency) financial data. Under the conditional Wishart assumption for a quite general realized multivariate volatility model, we provide both conditional and unconditional asymptotic distributions of the vectorized realized covariance matrix computed on the daily basis. Then, for a given day, it is of interest to test whether the pre-selected multivariate volatility model suits to observed realized measures. For this purpose we suggest statistical tests for the unconditional expectation of vectorized realized covariance matrix based on either Euclidean or Mahalanobis distances, and provide the asymptotic distributions of the test statistics under the null distribution. Our Monte Carlo simulation study shows that the unconditional test based on the Mahalanobis distance exhibits decent power for detecting deviations from the model-based unconditional expectation vector due to shifts either in variances or in correlations. Therefore, we recommend this test for use in empirical applications.