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Estimation for the discretely observed telegraph process


  • Stefano Iacus

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

  • Nakahiro Yoshida

    (Graduate School of Mathematical Sciences, University of Tokyo)


The telegraph process {X(t), t>0}, is supposed to be observed at n+1 equidistant time points t_i=i Delta_n,i=0,1,... , n. The unknown value of lambda, the underlying rate of the Poisson process, is a parameter to be estimated. The asymptotic framework considered is the following: Delta_n -> 0, n Delta_n = T -> infty as n -> infty. We show that previously proposed moment type estimators are consistent and asymptotically normal but not efficient. We study further an approximated moment type estimator which is still not efficient but comes in explicit form. For this estimator the additional assumption n Delta_n^3 -> 0 is required in order to obtain asymptotic normality. Finally, we propose a new estimator which is consistent, asymptotically normal and asymptotically efficient under no additional hypotheses.

Suggested Citation

  • Stefano Iacus & Nakahiro Yoshida, 2006. "Estimation for the discretely observed telegraph process," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1045, Universit√° degli Studi di Milano.
  • Handle: RePEc:bep:unimip:unimi-1045
    Note: oai:cdlib1:unimi-1045

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    Cited by:

    1. Alessandro Gregorio & Stefano Iacus, 2008. "Parametric estimation for the standard and geometric telegraph process observed at discrete times," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 249-263, October.
    2. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849,, revised Dec 2014.


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