We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed-form or can be approximated accurately for many popular continuous-time Markov models in economics andfinance. An omnibus test procedure fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time alternatives in the multifactor framework. A class of easy-to-interpret diagnostic procedures is also proposed to gauge possible sources of model misspecifications. All our test statistics have a convenient asymptotic N(0; 1) distribution under correct model specification. Simulations show that our tests have reasonable size, thanks to the dimension reduction in nonparametric regression, and good power against a variety of alternatives, including misspecifications in the joint dynamics even if the dynamics of each individual component is correctly specified. This feature is not attainable by some existing tests. A parametric bootstrap improves the finite sample performance of proposed tests, but with higher computational costs.
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