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Change point estimation for the telegraph process observed at discrete times

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Author Info
Alessandro De Gregorio (Università di Milano, Italy)
Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT)

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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.

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Publisher Info
Paper provided by Universitá degli Studi di Milano in its series UNIMI - Research Papers in Economics, Business, and Statistics with number 1053.

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Date of creation: 03 May 2007
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Handle: RePEc:bep:unimip:1053

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Related research
Keywords: discrete observations; change point problem; volatility regime switch; telegraph process;

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  1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November. [Downloadable!] (restricted)
  2. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor and Francis Journals, vol. 7(5), pages 575-583. [Downloadable!] (restricted)
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  3. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October. [Downloadable!] (restricted)
  4. Nikita Ratanov, 2005. "Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts," BORRADORES DE INVESTIGACIÓN 003410, UNIVERSIDAD DEL ROSARIO - FACULTAD DE ECONOMÍA. [Downloadable!]
  5. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May. [Downloadable!] (restricted)
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