2007/02/28 by Song Xi Chen, Jiti Gao, Cheng Yong Tang · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #Stochastic processes and financial applications #math.ST #msc:62G05 #msc:62J02 #stat.TH
paper · pdf · doi:10.1214/009053607000000659
published as Annals of Statistics 2008, Vol. 36, No. 1, 167-198 · Published in at http://dx.doi.org/10.1214/009053607000000659 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/02/01 · arxiv created 2008/03/12 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
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.