A test for model specification of diffusion processes

被引:59
作者
Chen, Song Xi [1 ]
Gao, Jiti [2 ]
Tang, Cheng Yong [1 ]
机构
[1] Iowa State Univ, Dept Stat, Ames, IA 50011 USA
[2] Univ Western Australia, Sch Math & Stat, Crawley, WA 6009, Australia
关键词
bootstrap; diffusion process; empirical likelihood; goodness-of-fit test; time series; transitional density;
D O I
10.1214/009053607000000659
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:167 / 198
页数:32
相关论文
共 47 条
[11]  
CHEN SX, 2007, IN PRESS J ECONOMETR
[12]  
CHEN SX, 2007, TEST MODEL SPECIFICA
[13]   A THEORY OF THE TERM STRUCTURE OF INTEREST-RATES [J].
COX, JC ;
INGERSOLL, JE ;
ROSS, SA .
ECONOMETRICA, 1985, 53 (02) :385-407
[14]  
Fan J., 2003, NONLINEAR TIME SERIE
[15]  
Fan J., 1996, LOCAL POLYNOMIAL MOD
[16]  
FAN J, 2004, ANN STAT, V29, P153
[17]   Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems [J].
Fan, JQ ;
Yao, QW ;
Tong, H .
BIOMETRIKA, 1996, 83 (01) :189-206
[18]   A selective overview of nonparametric methods in financial econometrics [J].
Fan, JQ .
STATISTICAL SCIENCE, 2005, 20 (04) :317-337
[19]   A crossvalidation method for estimating conditional densities [J].
Fan, JQ ;
Yim, TH .
BIOMETRIKA, 2004, 91 (04) :819-834
[20]   A reexamination of diffusion estimators with applications to financial model validation [J].
Fan, JQ ;
Zhang, CM .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2003, 98 (461) :118-134