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Least squares volatility change point estimation for partially observed diffusion processes
Alessandro De Gregorio, Department of Economics, Business and Statistics, Università di Milano, Italy
Stefano Iacus, Department of Economics, Business and Statistics, University of Milan, IT
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ABSTRACT:
A one dimensional diffusion process X={X_t, 0 <= t <= T}, with drift b(x) and diffusion coefficient s(theta, x)=sqrt(theta) s(x) known up to theta>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.
SUGGESTED CITATION:
Alessandro De Gregorio and Stefano Iacus,
"Least squares volatility change point estimation for partially observed diffusion processes"
(September 2007).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 29.
http://services.bepress.com/unimi/statistics/art29
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