A test for model specification of diffusion processes
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.
|Date of creation:||Nov 2005|
|Date of revision:||Feb 2007|
|Publication status:||Published in Annals of Statistics 1.36(2008): pp. 162-198|
|Contact details of provider:|| Postal: |
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
- Andrew W. Lo, 1986.
"Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data,"
NBER Technical Working Papers
0059, National Bureau of Economic Research, Inc.
- Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
- Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
- Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
- Robinson, P M, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 511-34, October.
- Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
- Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
- Jianqing Fan & Qiwei Yao & Howell Tong, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
- Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-87.
- H. G. Müller & U. Stadtmüller, 1999. "Multivariate boundary kernels and a continuous least squares principle," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 439-458.
- Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
- Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(05), pages 615-645, October.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:11976. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)
If references are entirely missing, you can add them using this form.