Self-exciting hysteretic binomial autoregressive processes

Kai Yang, Xiuyue Zhao, Xiaogang Dong () and Christian H. Weiß
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Kai Yang: Changchun University of Technology
Xiuyue Zhao: Changchun University of Technology
Xiaogang Dong: Changchun University of Technology
Christian H. Weiß: Helmut Schmidt University

Statistical Papers, 2024, vol. 65, issue 3, No 3, 1197-1231

Abstract: Abstract This paper introduces an observation-driven integer-valued time series model, in which the underlying generating stochastic process is binomially distributed conditional on past information in the form of a hysteretic autoregressive structure. The basic probabilistic and statistical properties of the model are discussed. Conditional least squares, weighted conditional least squares, and maximum likelihood estimators are obtained together with their asymptotic properties. A search algorithm for the two boundary parameters, and the corresponding strong consistency of the estimators, are also provided. Finally, some numerical results on the estimators and a real-data example are presented.

Keywords: Integer-valued time series; Hysteretic autoregressive model; Binomial autoregression; Parameter estimation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01444-x

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