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Change point estimation for the telegraph process observed at discrete times

Author

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  • Alessandro De Gregorio

    (Università di Milano, Italy)

  • Stefano Iacus

    (Department of Economics, Business and Statistics, University of Milan, IT)

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.

Suggested Citation

  • Alessandro De Gregorio & Stefano Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1053, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1053
    Note: oai:cdlib1:unimi-1053
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    References listed on IDEAS

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    6. Nikita Ratanov, 2005. "Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts," Borradores de Investigación 3410, Universidad del Rosario.
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    Cited by:

    1. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Papers 0812.0761, arXiv.org.

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