Multivariate specification tests based on a dynamic Rosenblatt transform

This paper considers parametric model adequacy tests for nonlinear multivariate dynamic models. It is shown that commonly used Kolmogorov-type tests do not take into account cross-sectional nor time-dependence structure, and a test, based on multi-parameter empirical processes, is proposed that overcomes these problems. The tests are applied to a nonlinear LSTAR-type model of joint movements of UK output growth and interest rate spreads. A simulation experiment illustrates the properties of the tests in finite samples. Asymptotic properties of the test statistics under the null of correct specification and under the local alternative, and justification of a parametric bootstrap to obtain critical values, are provided.