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Parametric estimation for partially hidden diffusion processes sampled at discrete times
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
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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, and Nakahiro Yoshida,
"Parametric estimation for partially hidden diffusion processes sampled at discrete times"
(November 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 18.
http://services.bepress.com/unimi/statistics/art18
Paper presented by P. Ferrari.
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