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CHARACTERISTIC FUNCTION–BASED TESTING FOR MULTIFACTOR CONTINUOUS-TIME MARKOV MODELS VIA NONPARAMETRIC REGRESSION

Published online by Cambridge University Press:  04 November 2009

Bin Chen*
Affiliation:
University of Rochester
Yongmiao Hong*
Affiliation:
Cornell University and Xiamen University
*
*Address correspondence to Bin Chen, Department of Economics, University of Rochester, Rochester, NY 14627, USA; e-mail: bchen8@mail.rochester.edu
Yongmiao Hong, Departments of Economics and Statistical Science, Cornell University, Ithaca, NY 14850, USA; e-mail: yh20@cornell.edu.

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.

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ARTICLES
Copyright
Copyright © Cambridge University Press 2009

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CHARACTERISTIC FUNCTION–BASED TESTING FOR MULTIFACTOR CONTINUOUS-TIME MARKOV MODELS VIA NONPARAMETRIC REGRESSION
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