Estimation of generalized threshold autoregressive models

Rongmao Zhang, Qimeng Liu and Jianhua Shi

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 18, 6456-6474

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.

Date: 2023
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DOI: 10.1080/03610926.2022.2029896

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