A test for model specification of diffusion processes

• 成果类型: Article
• 署名作者: Chen, Song Xi; Gao, Jiti; Tang, Cheng Yong
• 署名单位: Iowa State University; University of Western Australia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000659
• 发表日期: 2008
• 页码: 167-198
• 关键词: of-fit tests; maximum-likelihood-estimation; CONTINUOUS-TIME MODELS; Empirical Likelihood; nonparametric-estimation; term structure; regression; densities

摘要

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.