Multivariate Specification Tests Based on a Dynamic Rosenblatt Transform

This paper considers parametric model adequacy tests for nonlinear multivariate dynamic models. We show that commonly used Kolmogorov type tests do not take into account cross-sectional nor time dependence structure and... [ view full abstract ]

This paper considers parametric model adequacy tests for nonlinear multivariate dynamic models. We show that commonly used Kolmogorov type tests do not take into account cross-sectional nor time dependence structure and propose a test based on multi-parameter empirical processes that overcomes these problems. We propose a simulation experiment to illustrate the properties of the tests. The tests are applied to a nonlinear LSTAR-type model of joint movements of the UK output growth and interest rate spreads. 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.