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May 2021 Modeling Z-valued time series based on new versions of the Skellam INGARCH model
Yan Cui, Qi Li, Fukang Zhu
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Braz. J. Probab. Stat. 35(2): 293-314 (May 2021). DOI: 10.1214/20-BJPS473


Recently, there has been a growing interest in integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, but only a few of them can deal with data on the full set of integers, that is, Z={,2,1,0,1,2,}. Although some attempts have been made to deal with Z-valued time series, these models do not provide enough flexibility in modeling some specific integers (e.g., 0, ±1). A symmetric Skellam INGARCH(1,1) model was proposed in the literature, but it only considered zero-mean processes, which limits its application. We first extend the symmetric Skellam INGARCH model to an asymmetric version, which can deal with non-zero-mean processes. Then we propose a modified Skellam model which adopts a careful treatment on integers 0 and ±1 to satisfy a special feature of the data. Our models are easy-to-use and flexible. The maximum likelihood method is used to estimate unknown parameters and the log-likelihood ratio test statistic is provided for testing the asymmetric model against the modified one. Simulation studies are given to evaluate performances of the parametric estimation and log-likelihood ratio test. A real data example is also presented to demonstrate good performances of newly proposed models.


We are very grateful to the Editor, Associate Editor and anonymous referees for providing several constructive comments which led to a significant improvement of the paper. Zhu’s work is supported by National Natural Science Foundation of China (Nos. 11871027, 11731015), and Cultivation Plan for Excellent Young Scholar Candidates of Jilin University. Li’s work is supported by Natural Science Foundation of Changchun Normal University (No. 2018-004). Zhu is the corresponding author.


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Yan Cui. Qi Li. Fukang Zhu. "Modeling Z-valued time series based on new versions of the Skellam INGARCH model." Braz. J. Probab. Stat. 35 (2) 293 - 314, May 2021.


Received: 1 June 2019; Accepted: 1 April 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.1214/20-BJPS473

Keywords: 0 and ±1 inflations , INGARCH processes , modified Skellam , Skellam , Z-valued time series

Rights: Copyright © 2021 Brazilian Statistical Association


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Vol.35 • No. 2 • May 2021
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