Estimation for the change point of volatility in a stochastic differential equation
Estimation for the change point of volatility in a stochastic differential equation
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DOI：
10.1016/j.spa.2011.11.005
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发表时间：
2012-03-01
影响因子：
1.4
通讯作者：
Yoshida, Nakahiro
中科院分区：
文献类型：
--
作者：
Iacus, Stefano M.;Yoshida, Nakahiro
我们考虑一个多维Ito过程Y=(Y-t)(t是[0，T]的一个元素)，它具有一些未知的漂移系数过程b(T)和波动系数sigma(X-t，theta)，其中协变量过程X=(X-t)(t是[0，T]的一个元素)，函数a(x，直到theta已知)是theta的一个元素。对于这个模型，我们考虑了波动率分量中参数theta的变点问题。这种变化应该在某一时刻发生，L*是(0，T)的一个元素。在给定过程(X，Y)的离散时间观测值的情况下，我们提出了变点的拟极大似然估计。给出了变点估计的收敛速度和渐近混合型极限定理。(C)2011爱思唯尔B.V.保留所有权利。
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.