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Article

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, China
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Entropy 2021, 23(1), 62; https://doi.org/10.3390/e23010062
Received: 29 October 2020 / Revised: 28 December 2020 / Accepted: 28 December 2020 / Published: 31 December 2020
(This article belongs to the Special Issue Time Series Modelling)
The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model. View Full-Text
Keywords: extended binomial distribution; INAR; thinning operator; time series of counts extended binomial distribution; INAR; thinning operator; time series of counts
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MDPI and ACS Style

Liu, Z.; Zhu, F. A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data. Entropy 2021, 23, 62. https://doi.org/10.3390/e23010062

AMA Style

Liu Z, Zhu F. A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data. Entropy. 2021; 23(1):62. https://doi.org/10.3390/e23010062

Chicago/Turabian Style

Liu, Zhengwei, and Fukang Zhu. 2021. "A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data" Entropy 23, no. 1: 62. https://doi.org/10.3390/e23010062

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