Open Access
February 2008 A test for model specification of diffusion processes
Song Xi Chen, Jiti Gao, Cheng Yong Tang
Ann. Statist. 36(1): 167-198 (February 2008). DOI: 10.1214/009053607000000659


We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth choice, the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths. To better capture the finite sample distribution of the test statistic and data dependence, the critical value of the test is obtained by a parametric bootstrap procedure. Properties of the test are evaluated asymptotically and numerically by simulation and by a real data example.


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Song Xi Chen. Jiti Gao. Cheng Yong Tang. "A test for model specification of diffusion processes." Ann. Statist. 36 (1) 167 - 198, February 2008.


Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1132.62063
MathSciNet: MR2387968
Digital Object Identifier: 10.1214/009053607000000659

Primary: 62G05
Secondary: 62J02

Keywords: bootstrap , diffusion process , empirical likelihood , Goodness-of-fit test , time series , transitional density

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • February 2008
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