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Change point estimation for the telegraph process observed at discrete times

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Author Info
Alessandro De Gregorio
Stefano M. Iacus

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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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File URL: http://arxiv.org/abs/0705.0503
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File URL: http://arxiv.org/pdf/0705.0503
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0705.0503.

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Date of creation: May 2007
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Handle: RePEc:arx:papers:0705.0503

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Quantitative Finance Papers 0812.0761, arXiv.org. [Downloadable!]
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