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

Xiong, Lanyu; Zhu, Fukang

doi:10.1007/s00180-022-01293-6

Cited by 5 publications

(4 citation statements)

References 36 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

Stat

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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

Stat

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“…The estimation of model coefficients oriented by a GARCH model gives us the estimated data with the following Table 5, where a is the true value of model (32), â is its estimators, and ns represents the number of simulations It can be observed that estimators of variable values in the bilinear model, as defined by its expression, yield efficient results when driven by Symmetric GARCH compared to Asymmetric GARCH, indicating that symmetry plays a crucial role in enhancing the accuracy of estimation for the proposed model [19][20][21][22][23][24][25].…”

Section: Asymmetric and Symmetric Garch Modelsmentioning

confidence: 99%

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

Abu Hammad,

Alkhateeb,

Laiche

et al. 2024

Symmetry

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This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.

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“…Li et al [ 59 ] proposed a new loss function by twofold improvement. Along similar lines, Xiong and Zhu [ 60 ] introduced a robust estimation for the one-parameter exponential family INGARCH(1,1) models.…”

Section: Count Time Seriesmentioning

confidence: 99%

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

Cited by 5 publications

References 36 publications

Softplus negative binomial network autoregression

Softplus negative binomial network autoregression

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

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

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