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Change point estimation for the telegraph process observed at discrete times

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  • Alessandro De Gregorio
  • Stefano M. Iacus

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 M. Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," Papers 0705.0503, arXiv.org.
    • Handle: RePEc:arx:papers:0705.0503
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    1. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
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    5. 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.
    6. Dean W. Wichern & Robert B. Miller & Der‐Ann Hsu, 1976. "Changes of Variance in First‐Order Autoregressive Time Series Models—With an Application," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 248-256, November.
    7. 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.
    8. 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.
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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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