A Test for Model Specification of Diffusion Processes

• Published in: The Annals of statistics 2008-02, Vol.36 (1), p.167-198
• Main Authors: Chen, Song Xi, Gao, Jiti, Tang, Cheng Yong
• Format: Article
• Language: English
• Subjects: 62G05; 62J02; Bootstrap; Bootstrap method; Combinatorics; Combinatorics. Ordered structures; Data smoothing; Density; Density estimation; diffusion process; Economic models; empirical likelihood; Estimating techniques; Estimators; Exact sciences and technology; General topics; goodness-of-fit test; Graph theory; Markov processes; Mathematical models; Mathematics; Maximum likelihood method; Nonparametric inference; Nonparametric models; Parameter estimation; Parametric models; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistical theories; Statistics; time series; Time series models; transitional density
• ISSN: 0090-5364; 2168-8966
• DOI: 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 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.