Abstract
This paper proposes a kernel estimator for the coefficient of multidimensional time-varying diffusion processes as an extension of the estimation model for one dimensional diffusion coefficient to the multidimensional case. By using “time division”, the authors overcome the problem of sample observation in time varying model. In addition, the authors prove the strong consistency and limit distribution of the estimator. Finally, the authors test the performance of the estimator through a simulation experiment and an empirical application.
Similar content being viewed by others
References
Genon-Gatalot V and Jacod J, On the estimation of the diffusion coefficient for multidimensional diffusion processes, Ann. Inst. H. Poincare Probab. Statist., 1993, 29: 119–151.
Ait-Sahalia Y, Closed-form likelihood expansions for multivariate diffusions, The Annals of Statistics, 2008, 36: 906–937.
Brugire P, Thorme de limite centrale pour un estimateur nonparamtrique de la variance d'un processus de diffusion multidimensionnelle, Ann. Inst. Henri. Poincare, 1993, 29: 357–389.
Chen P and Feng Y, Nonparametric estimation model of the drift vector and the diffusion matrix, Chinese Journal of Contemporary Mathematics, 2011, 32(4): 497–506.
Fan J Q, Jiang J C, Zhang C M, et al., Time-dependent diffusion models for term structure dynamics, Statistica Sinica, 2003, 13: 965–992.
Black F, Derman E, and Toy W, A one-factor model of interest rates and its application to treasury bond options, Financial Analysts Journal, 1990, 46(1): 33–39.
Black F and Karasinski P, Bond and option pricing when short rates are lognormal, Financial Analysts Journal, 1991, 47(4): 52–59.
Donoho D L, Johnstone I M, Kerkyacharian G, et al., Density estimation by wavelet thresholding, The Annals of Statistics, 1996, 24(2): 508–539.
Chen X, Hansen L P, and Carrasco M, Nonlinearity and temporal dependence, Econometrics, 2010, 155: 155–169.
Ait-Sahalia Y and Joon Y P, Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models, Journal of Econometrics, 2016, 192: 119–138.
Bandi F M and Phillips P C B, Fully nonparametric estimation of scalar diffusion models, Econometrica, 2003, 71: 241–283.
Karatzas I and Shreve S E, Brownian Motion and Stochastic Calculus, 2nd Edition, Springer, New York, 1991.
Hall P and Heyde C C, Martingle Limit Theory and Its Application, Academic Press, New York, 1980.
Knight F B, A Reduction of Continuous Square Integrable Martingales to Brownian Motion, Springer, Berlin, 1971.
Author information
Authors and Affiliations
Corresponding authors
Additional information
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11271189 and 11201229.
This paper was recommended for publication by Editor DONG Yuexiao.
Rights and permissions
About this article
Cite this article
Wang, J., Chen, P. Nonparametric Estimation for the Diffusion Coefficient of Multidimensional Time-Varying Diffusion Processes. J Syst Sci Complex 33, 1602–1631 (2020). https://doi.org/10.1007/s11424-020-8376-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-020-8376-9