ON PARAMETER ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESS

Volume 1, Issue 1, October 2016     |     PP. 119-129      |     PDF (335 K)    |     Pub. Date: November 13, 2016
DOI:    401 Downloads     7754 Views  

Author(s)

LabadzeLevan, Georgian Technical University
SokhadzeGrigol, I.Javakhishvili Tbilisi State University
KvatadzeZurab, I.Javakhishvili Tbilisi State University

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.