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Estimation of generalized threshold autoregressive models

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  • Rongmao Zhang
  • Qimeng Liu
  • Jianhua Shi

Abstract

In this article, the maximum likelihood estimate and Bayesian estimate for a general threshold autoregressive model are considered. It is shown that under certain regular conditions, the maximum likelihood estimator (MLE) and Bayesian estimator (BE) of the threshold parameters are super consistent with convergence rate n. And the moments of the Bayesian estimator exist when the corresponding moments of the noise are finite and its limit distribution is a functional of integrated compound Poisson processes. Furthermore, the estimators of the regression parameters are shown to be asymptotically normal with convergence rate n. Two simulations are conducted to compare the BE with MLE.

Suggested Citation

  • Rongmao Zhang & Qimeng Liu & Jianhua Shi, 2023. "Estimation of generalized threshold autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(18), pages 6456-6474, September.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:18:p:6456-6474
    DOI: 10.1080/03610926.2022.2029896
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