ON PARAMETER ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESS
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Author(s)
Abstract
An estimation procedure for Ornstein–Uhlenbeck process drift and volatility coefficients is given. The procedure is based on the maximum likelihood principle andplug-in-estimator.
Keywords
Estimation,MLE,Ornstein-Uhlenbeck processes, plug-in-estimator.
Cite this paper
LabadzeLevan, SokhadzeGrigol, KvatadzeZurab,
ON PARAMETER ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESS
, SCIREA Journal of Mathematics.
Volume 1, Issue 1, October 2016 | PP. 119-129.
References
[ 1 ] | Athreya S. R., Bass R. F., Gordina M., Perkins E. A. Infinite Dimensional Stochastic Differential Equations of Ornstein-Uhlenbeck Type. Stochastic Processes and their Applications, 116, 381–406. 2006. |
[ 2 ] | Babilua P., Nadaraya E., Sokhadze G. On the limit properties of maximal likelihood estimators in a Hilbert space. Georgian Mathematical Journal. Vol. 22, Issue 2. 171-178, 2015 |
[ 3 ] | Benguria R., Kac M. Quantum Langevin Equation. Physical Review Letters, 46, p. 1-4. 1981. |
[ 4 ] | Bishwal J. P. Parameter Estimation in Stochastic Differential Equations. Springer-Verlag Berlin Heidelberg. 2008. |
[ 5 ] | Brouste A., Iacus S. M. Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package. arXiv:1112.3777v1. |
[ 6 ] | Curtain R. Markov Processes Generated by Linear Stochastic Evolution Equations. Stochastics, 5, p. 135-165. 1981. |
[ 7 ] | Daletskiy Y. L., Belopol’skaya Y. I. Stochastic Equations and Differential Geometry (in Russian), VyshchaShkola, Kiev, 1989. |
[ 8 ] | Gao M. Free Ornstein-Uhlenbeck Processes. Journal of Mathematical Analysis and Applications, 322, p. 177-192. 2006. |
[ 9 ] | Gubeladze A., Sokhadze G. On the Maximum Likelihood Estimation of Stochastic Differential Equations. Proceedings of I. Vekua Institute of Applied Mathematics. Vol. 63. 1-7 2013. |
[ 10 ] | Kott T. Statistical Inference for Generalized Mean Reversion Processes.Diss. of Ruhr-niversitat Bochum. September. 2010. |
[ 11 ] | Liptser R.S., Shiryaev A.N. Statistics of Random Processes. Springer-Verlag. 1978. |
[ 12 ] | Maslowski B., Pospisil J. Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process. Applied Mathematics and Optimization. 57(3), 401-429. 2008. |
[ 13 ] | McKeague I. W. Estimation for Infinite Dimensional Ornstein-Uhlenbeck Processes. Florida State University Statistics Report No. M674. 9 p. 1983. |
[ 14 ] | Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration. Journal of Econometrics, Volume 172, Issue 2, p. 325–337. 2013. |
[ 15 ] | Stein E., Stein J. Stock Price Distribution with Stochastic Volatility: An Analytic Approach. Review of Financial Studies, 4(4), p. 727-752. 1991. |
[ 16 ] | Sokhadze G. On the Absolute Continuity of Smooth Measures. Theoryof Probability and Mathematical Statistics, 491996 |
[ 17 ] | Valdivieso L., Schoutens W., Tuerlinckx F. Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type. Stat. Infer Stoch Process, 12:1, p. 1-19. 2009. |
[ 18 ] | Walsh J. B. A Stochastic Model for Neural Response. Adv. Appl. Probability, 13, p. 231-281. 1981. |
[ 19 ] | Wittig T. A Dynamical Theory of Generalized Ornstein-Uhlenbeck Processes. Ph. D. dissertation, Michigan State University. 1981. |