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# Parametric estimation for partially hidden diffusion processes sampled at discrete times

## Author

Listed:
• 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
as

File URL: http://services.bepress.com/unimi/statistics/art18

## References listed on IDEAS

as
1. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
2. 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.
3. 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. repec:spr:sistpr:v:20:y:2017:i:2:d:10.1007_s11203-016-9142-4 is not listed on IDEAS
2. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.

### Keywords

discrete observations; partially observed systems; diffusion processes;

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