Least squares volatility change point estimation for partially observed diffusion processes

Alessandro De Gregorio and Stefano Iacus ()
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Alessandro De Gregorio: Department of Economics, Business and Statistics, Università di Milano, Italy

No unimi-1063, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

Abstract: A one dimensional diffusion process X={X_t, 0 0, is supposed to switch volatility regime at some point t* in (0,T). On the basis of discrete time observations from X, the problem is the one of estimating the instant of change in the volatility structure t* as well as the two values of theta, say theta_1 and theta_2, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length Delta_n with n*Delta_n=T. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant.

Keywords: discrete observations; diffusion process; change point problem; volatility regime switch; nonparametric estimator (search for similar items in EconPapers)
Date: 2007-09-18
Note: oai:cdlib1:unimi-1063
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