Parametric estimation for partially hidden diffusion processes sampled at discrete times

Stefano Iacus (siacus@iq.harvard.edu), Masayuki Uchida and Nakahiro Yoshida
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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

No unimi-1042, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

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.

Keywords: discrete observations; partially observed systems; diffusion processes (search for similar items in EconPapers)
Date: 2006-11-12
Note: oai:cdlib1:unimi-1042
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Citations: View citations in EconPapers (1)

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Journal Article: Parametric estimation for partially hidden diffusion processes sampled at discrete times (2009)
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