Bootstrap specification tests for multivariate GARCH processes

Music City Center 

We develop tests for the correct specification of the conditional distribution in multivariate GARCH models based on empirical processes. We transform the multivariate data into univariate data based on the marginal and conditional cumulative distribution functions specified by the null model. The test statistics considered are based on empirical processes of the transformed data in the presence of estimated parameters. The limiting distributions of the proposed test statistics are model dependent and are not free from the underlying nuisance parameters, making the tests difficult to implement. To address this, we develop a novel bootstrap procedure which is shown to be asymptotically valid irrespective of the presence of nuisance parameters. This approach utilises a particular scalable iterated bootstrap method and is simple to implement as the associated test statistics have simple closed form expressions. A simulation study demonstrates that the new tests perform well in finite samples. A real data example illustrates the testing procedure.

Bootstrap

Multivariate GARCH

Specification test 

Business and Economic Statistics Section