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Parametric estimation for partially hidden diffusion processes sampled at discrete times

Author

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  • Stefano Iacus

    (Department of Economics, Business and Statistics, University of Milan, IT)

  • Masayuki Uchida

    (Departement of Mathematical Sciences, Faculty of Mathematics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan)

  • Nakahiro Yoshida

    (Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914 Japan)

Abstract

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$ is observed only when its path lies over some threshold $\tau$. On the basis of the observable part of the trajectory, the problem is to estimate finite dimensional parameter in both drift and diffusion coefficient under a discrete sampling scheme. It is assumed that the sampling occurs at regularly spaced times intervals of length $h_n$ such that $h_n\cdot n =T$. The asymptotic is considered as $T\to\infty$, $n\to\infty$, $n h_n^2\to 0$. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficient is proved.

Suggested Citation

  • Stefano Iacus & Masayuki Uchida & Nakahiro Yoshida, 2006. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1042, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1042
    Note: oai:cdlib1:unimi-1042
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    References listed on IDEAS

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    1. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777, September.
    2. Yong Zeng, 2003. "A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 411-444, July.
    3. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    4. Stefano M. Iacus & Ilia Negri, 2003. "Estimating unobservable signal by Markovian noise induction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(2), pages 153-167, December.
    5. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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    Cited by:

    1. Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.
    2. Shen, Leyi & Xia, Xiaoyu & Yan, Litan, 2022. "Least squares estimation for the linear self-repelling diffusion driven by α-stable motions," Statistics & Probability Letters, Elsevier, vol. 181(C).
    3. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    4. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.

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