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On parameter estimation of threshold autoregressive models

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Abstract

This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit likelihood ratio. Furthermore, convergence of moments of the estimators is also established. The limit distribution can be computed via explicit simulations from which testing and inference for the threshold parameter can be conducted. The obtained results are illustrated with numerical simulations.

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Authors and Affiliations

  1. Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Ngai Hang Chan

  2. Laboratoire de Statistique et Processus, Université du Maine, 72085, Le Mans Cedex 9, France

    Yury A. Kutoyants

Authors
  1. Ngai Hang Chan
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  2. Yury A. Kutoyants
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Correspondence to Ngai Hang Chan.

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Chan, N.H., Kutoyants, Y.A. On parameter estimation of threshold autoregressive models. Stat Inference Stoch Process 15, 81–104 (2012). https://doi.org/10.1007/s11203-011-9064-0

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  • DOI: https://doi.org/10.1007/s11203-011-9064-0

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