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May 2020 Random environment binomial thinning integer-valued autoregressive process with Poisson or geometric marginal
Zhengwei Liu, Qi Li, Fukang Zhu
Braz. J. Probab. Stat. 34(2): 251-272 (May 2020). DOI: 10.1214/18-BJPS421

Abstract

To predict time series of counts with small values and remarkable fluctuations, an available model is the $r$ states random environment process based on the negative binomial thinning operator and the geometric marginal. However, we argue that the aforementioned model may suffer from the following two drawbacks. First, under the condition of no prior information, the overdispersed property of the geometric distribution may cause the predictions fluctuate greatly. Second, because of the constraints on the model parameters, some estimated parameters are close to zero in real-data examples, which may not objectively reveal the correlation relationship. For the first drawback, an $r$ states random environment process based on the binomial thinning operator and the Poisson marginal is introduced. For the second drawback, we propose a generalized $r$ states random environment integer-valued autoregressive model based on the binomial thinning operator to model fluctuations of data. Yule–Walker and conditional maximum likelihood estimates are considered and their performances are assessed via simulation studies. Two real-data sets are conducted to illustrate the better performances of the proposed models compared with some existing models.

Citation

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Zhengwei Liu. Qi Li. Fukang Zhu. "Random environment binomial thinning integer-valued autoregressive process with Poisson or geometric marginal." Braz. J. Probab. Stat. 34 (2) 251 - 272, May 2020. https://doi.org/10.1214/18-BJPS421

Information

Received: 1 July 2018; Accepted: 1 October 2018; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232928
MathSciNet: MR4093258
Digital Object Identifier: 10.1214/18-BJPS421

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 2 • May 2020
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