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Estimation for the change point of the volatility in a stochastic differential equation
Stefano Iacus, Department of Economics, Business and Statistics, University of Milan, IT
Nakahiro Yoshida, Graduate School of Mathematical Sciences, Tokyo University, Tokyo
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ABSTRACT:
We consider a multidimensional Ito process Y=(Y_t), t in [0,T], with some unknown drift coefficient process b_t and volatility coefficient sigma(X_t,theta) with covariate process X=(X_t), t in[0,T], the function sigma(x,theta) being known up to theta in 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 t* in (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 thereoms of aymptotically mixed type.
SUGGESTED CITATION:
Stefano Iacus and Nakahiro Yoshida,
"Estimation for the change point of the volatility in a stochastic differential equation"
(June 2009).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 44.
http://services.bepress.com/unimi/statistics/art44
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