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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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.
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