A test for model specification of diffusion processes

Details A test for model specification of diffusion processes A test for model specification of diffusion processes

2007-02-06

arxiv.org/abs/math/0702123v2

Annals of Statistics 2008, Vol. 36, No. 1, 167-198

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000659 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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 $L_2$-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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