Tail asymptotics for the bivariate equi-skew generalized hyperbolic distribution and its Variance-Gamma special case

Fung, Thomas; Seneta, E.

doi:10.1016/j.spl.2021.109182

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Within various disciplines such as business, economics, finance, insurance, and related fields, one can find symmetric, elliptical, skew-elliptical, and various other distributions, as well as their corresponding regression and time series models. Examples of such works include ; Liu and Heyde (2008); Liu et al (2011Liu et al ( , 2015Liu et al ( , 2020Liu et al ( , 2022a, and Fung and Seneta (2021). Elliptical and skew-elliptical regression models find applications in statistical inference, sensitivity analysis, local influence diagnostics, and other areas.…”

Section: Introductionmentioning

confidence: 99%

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

Dewick

Liu

et al. 2023

JRFM

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Various statistical distributions have played significant roles in financial data analytics in recent decades. Among these, elliptical modeling has gained popularity, while the study and application of skew-elliptical modeling have garnered increased attention in various domains. This paper begins by acknowledging the notable accomplishments and contributions of Professor Chris Heyde in the field of financial data modeling. We provide a comprehensive review of elliptical and skew-elliptical modeling, summarizing the latest advancements. In particular, we focus on the characteristics, estimation methods, and diagnostics of elliptical and skew-elliptical distributions in regression and time series models, as well as copula modeling. Furthermore, we discuss several related applications in regression and time series models, including estimation and diagnostic methods. The main objective of this paper is to address the critical need for accurately identifying the underlying elliptical distribution, whether it is elliptical or skew-elliptical. This identification is essential for conducting local influence diagnostics and employing appropriate regression methods using suitable elliptical modeling techniques. To illustrate this process, we present examples that demonstrate the identification of the elliptical distribution, starting with the Box–Jenkins methodology and progressing to copula modeling. The inclusion of copula modeling is motivated by its effectiveness in conjunction with elliptical and skew-elliptical distributions, as it aids in distinguishing between the two. Ultimately, the findings of this paper offer valuable insights, as correctly determining the elliptical and skew-elliptical distribution enables the application of suitable local influence and regression methods, thereby contributing to financial portfolio management, business analytics, and insurance analytics, ensuring the accurate specification of models.

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Section: Introductionmentioning

confidence: 99%

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

Dewick

Liu

et al. 2023

JRFM

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On Familywise Error Rate Cutoffs under Pairwise Exchangeability

Fung

Seneta

2023

Methodol Comput Appl Probab

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In a pairwise exchangeable dependence setting for test statistics, the cutoffs of Sarkar et al. (2016) may be viewed as a first iteration improvement of Holm (1979)’s classical cutoffs under a convexity condition on the copula. The cutoffs of Seneta and Chen (1997) which improve Holm’s in the present exchangeability setting, are shown, after an analogous first iteration step, to lead to a refinement of Sarkar et al. (2016). Further, we show that the convexity condition can be circumvented in practice, computationally. Improvement by iteration limit of cutoffs is considered for both procedures. Comparisons between the effects of the several cutoff sets are made by way of plots of the familywise error rate against correlation $$\rho$$ ρ in the classic setting of the multivariate Normal; and the distributional setting of the multivariate Generalized Hyperbolic for the important Variance Gamma type subfamily, for which a convexity condition cannot be analytically verified.

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Tail asymptotics for the bivariate equi-skew generalized hyperbolic distribution and its Variance-Gamma special case

Cited by 2 publications

References 15 publications

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

On Familywise Error Rate Cutoffs under Pairwise Exchangeability

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