Minimum Density Power Divergence Estimator for Negative Binomial Integer-Valued GARCH Models

Xiong, Lanyu; Zhu, Fukang

doi:10.1007/s40304-020-00221-8

Cited by 15 publications

(3 citation statements)

References 33 publications

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“…When dealing with real-life data, extreme observations, not following the usual model, are commonly found. Other approaches to account for possible extreme observations include classical M-estimators or the recently published method by Li et al [22] or approaches based on the density power divergence, see for example Xiong and Zhu [23].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Stapper

2021

Entropy

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A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

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Section: Discussion and Outlookmentioning

confidence: 99%

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Stapper

2021

Entropy

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“…There are two advantages to this approach: the first is simplicity, i.e., it contains only a single tuning parameter that controls the trade-off between robustness and efficiency; the second is the ability to balance robustness and efficiency, providing considerable robustness while retaining high levels of efficiency as the tuning parameter approaches zero. Further, Xiong and Zhu [ 62 ] and Xiong and Zhu [ 63 ] used the Mallows’ quasi-likelihood estimator and the minimum density power dispersion estimator as a robust estimator for negative binomial INGARCH models, respectively. For negative binomial INGARCH models, Elsaied and Fried [ 64 ] also developed several robust estimators including robustifications of method of moments and ML-estimation, one of which was an alternative to the robust estimator proposed by Xiong and Zhu [ 63 ].…”

Section: Count Time Seriesmentioning

confidence: 99%

“…Further, Xiong and Zhu [ 62 ] and Xiong and Zhu [ 63 ] used the Mallows’ quasi-likelihood estimator and the minimum density power dispersion estimator as a robust estimator for negative binomial INGARCH models, respectively. For negative binomial INGARCH models, Elsaied and Fried [ 64 ] also developed several robust estimators including robustifications of method of moments and ML-estimation, one of which was an alternative to the robust estimator proposed by Xiong and Zhu [ 63 ].…”

Section: Count Time Seriesmentioning

confidence: 99%

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

Liu

Zhu

et al. 2023

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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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Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey’s biweight function

Xiong

Zhu

2022

Comput Stat

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Minimum Density Power Divergence Estimator for Negative Binomial Integer-Valued GARCH Models

Cited by 15 publications

References 33 publications

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

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

Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey’s biweight function

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