Diagnosing Multivariate Continuous-Time Models with Application to Affine Term Structure Models

Multivariate continuous-time models have been playing important roles in finance and economics. 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. Unlike the existing methods in the literature, the proposed omnibus 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. Simulation studies show that the tests provide reliable inference for sample sizes often encountered in finance and economics. The omnibus test has all-round power against various model misspecifications and the diagnostic tests can reveal useful information about the nature and type of model misspecification. In an application, we find that there is room for further improving upon a popular class of multivariate affine term structure models for monthly U.S. Treasury bond yields. It is documented that while there exists little dynamic structure in conditional means, there exist neglected dynamic structures in conditional variances and conditional correlations of yields with different maturities