The Annals of Statistics

A test for model specification of diffusion processes

Song Xi Chen, Jiti Gao, and Cheng Yong Tang

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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.

Article information

Ann. Statist., Volume 36, Number 1 (2008), 167-198.

First available in Project Euclid: 1 February 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62J02: General nonlinear regression

Bootstrap diffusion process empirical likelihood goodness-of-fit test time series transitional density


Chen, Song Xi; Gao, Jiti; Tang, Cheng Yong. A test for model specification of diffusion processes. Ann. Statist. 36 (2008), no. 1, 167--198. doi:10.1214/009053607000000659.

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