A Flexible Model for Time Series of Counts with Overdispersion or Underdispersion, Zero-Inflation and Heavy-Tailedness

Qian, Lianyong; Zhu, Fukang

doi:10.1007/s40304-022-00327-1

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…The model consider here can be extended in several directions. First, the negative binomial distribution can be generalized to one‐parameter exponential family distribution (Xiong & Zhu, 2023), generalized Conway–Maxwell–Poisson distribution (Qian & Zhu, 2023) or binomial‐discrete Poisson–Lindley distribution (Chesneau et al, 2022), among others; second, the network structure can be generalized to the one in Chen et al (2023). Third, it is a good idea to perform goodness‐of‐fit test based on the assumptions of the conditional distribution in the model.…”

Section: Discussionmentioning

confidence: 99%

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Softplus negative binomial network autoregression

Guo,

Zhu

2024

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Modelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones.

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Section: Discussionmentioning

confidence: 99%

“…The model consider here can be extended in several directions. First, the negative binomial distribution can be generalized to one-parameter exponential family distribution (Xiong & Zhu, 2023), generalized Conway-Maxwell-Poisson distribution (Qian & Zhu, 2023) or binomial-discrete…”

Section: Discussionmentioning

confidence: 99%

Softplus negative binomial network autoregression

Guo,

Zhu

2024

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“…See Table 1 for the specific definition of BNB. Relatedly, Qian and Zhu [ 8 ] was also concerned with heavy-tailed count time series and thus uses the generalized Conway–Maxwell–Poisson (GCOMP) distribution (in Table 1 ), which has one more parameter than the Conway–Maxwell–Poisson distribution, but provides a unified framework to handle over- or under-dispersed, zero-inflated, and heavy-tailed count data.…”

Section: Count Time Seriesmentioning

confidence: 99%

“…According to the properties of the GCOMP distribution, the approximate conditional expectation and variance are given by

and these are fundamentally the keys to the flexibility of the GCOMP-INGARCH

model. Qian and Zhu [ 8 ] also established some properties by assuming that model ( 2 ) is approximately stationary.…”

Section: Count Time Seriesmentioning

confidence: 99%

“…On the one hand, to model some specific features of count time series, researchers have innovated the conditional distribution assumption. Indeed, Gorgi [ 7 ] and Qian and Zhu [ 8 ] focus on heavy-tailed count time series, while Silva and Souza [ 9 ] is more concerned with the generality of distribution and Souza et al [ 10 ] further extends Silva and Souza [ 9 ] to the time-varying version. Accordingly, they all propose new conditional distribution assumptions that can model the features of interest.…”

Section: Introductionmentioning

confidence: 99%

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A Systematic Review of INGARCH Models for Integer-Valued Time Series

Liu

Zhu

et al. 2023

Entropy

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Count time series are widely available in fields such as epidemiology, finance, meteorology, and sports, and thus there is a growing demand for both methodological and application-oriented research on such data. This paper reviews recent developments in integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models over the past five years, focusing on data types including unbounded non-negative counts, bounded non-negative counts, Z-valued time series and multivariate counts. For each type of data, our review follows the three main lines of model innovation, methodological development, and expansion of application areas. We attempt to summarize the recent methodological developments of INGARCH models for each data type for the integration of the whole INGARCH modeling field and suggest some potential research topics.

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