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Change point estimation for the telegraph process observed at discrete times

Alessandro De Gregorio and Stefano Iacus ()
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Alessandro De Gregorio: Università di Milano, Italy

No unimi-1053, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

Abstract: The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or -v. The changes of direction are governed by an homogeneous Poisson process with rate lambda > 0. In this paper, we consider a change point estimation problem for the rate of the underlying Poisson process by means of least squares method. The consistency and the rate of convergence for the change point estimator are obtained and its asymptotic distribution is derived. Applications to real data are also presented.

Keywords: discrete observations; change point problem; volatility regime switch; telegraph process (search for similar items in EconPapers)
Date: 2007-05-03
Note: oai:cdlib1:unimi-1053
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