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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Abstract

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

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

Dates
First available in Project Euclid: 1 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1201877298

Digital Object Identifier
doi:10.1214/009053607000000659

Mathematical Reviews number (MathSciNet)
MR2387968

Zentralblatt MATH identifier
1132.62063

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1201877298


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