Abstract :
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 and finance. An omnibus test
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 misspecification. All the proposed
test statistics have a convenient asymptotic N(0,1) distribution under correct model
specification, and all asymptotic results allow for some data-dependent bandwidth.
Simulations show that in finite samples, 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, but 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 a higher computational cost.
