Generalized Spectral Testing for Multivariate Continuous-Time Models

We develop an omnibus specification test for multivariate continuous-time models using the conditional characteristic function, which often has a convenient closed-form or can be accurately approximated for many multivariate continuous-time models in finance and economics. The proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context. A class of easy-to-interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification. Our tests are also applicable to discrete-time distribution models. Simulation studies show that the tests provide reliable inference in finite samples.