Estimation for the change point of volatility in a stochastic differential equation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Iacus, Stefano M.¹  Yoshida, Nakahiro² 

[1] Univ Milan, Dept Econ Business & Stat, I-20122 Milan, Italy

[2] Univ Tokyo, Japan Sci & Technol Agcy, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

关键词: Ito processes;    Discrete time observations;    Change point estimation;    Volatility;   

DOI  :  10.1016/j.spa.2011.11.005

来源: Elsevier

【 摘 要 】

We consider a multidimensional Ito process Y = (Y-t)(t is an element of[0, T]) with some unknown drift coefficient process b(t) and volatility coefficient sigma(X-t, theta) with covariate process X = (X-t)(t is an element of[0, T]), the function a (x, being known up to theta is an element of Theta. For this model, we consider a change point problem for the parameter theta in the volatility component. The change is supposed to occur at some point l* is an element of (0, T). Given discrete time observations from the process (X, Y), we propose quasi-maximum likelihood estimation of the change point. We present the rate of convergence of the change point estimator and the limit theorems of the asymptotically mixed type. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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