IDEAS home Printed from https://ideas.repec.org/p/bep/unimip/unimi-1045.html
   My bibliography  Save this paper

Estimation for the discretely observed telegraph process

Author

Listed:
  • Stefano Iacus

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

  • Nakahiro Yoshida

    (Graduate School of Mathematical Sciences, University of Tokyo)

Abstract

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
    as

    Download full text from publisher

    File URL: http://services.bepress.com/unimi/statistics/art21
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, arXiv.org, revised Dec 2014.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bep:unimip:unimi-1045. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/damilit.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.