Asymmetric tail dependence modeling, with application to cryptocurrency market data

Gong, Yan; Huser, Raphaël

doi:10.1214/21-aoas1568

Cited by 15 publications

(3 citation statements)

References 48 publications

(53 reference statements)

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“…Mostly, authors used smooth transitions in other models, like smooth transition Generalized Autoregressive Conditionally Heteroskedastic (GARCH) models, to study asymmetric volatility in cryptocurrency markets [ 34 ]. Gong and Huser [ 35 ] applied asymmetric tail dependence models to test cryptocurrency market data. They also proposed a parsimonious copula model that keeps high flexibility in both the lower and upper tails of the cryptocurrency market.…”

Section: Literature Reviewmentioning

confidence: 99%

Dissecting Tether’s Nonlinear Dynamics during Covid-19

Maiti

Grubišić²,

Vuković

2020

Journal of Open Innovation: Technology, Market, and Complexity

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The present study is on the five cryptocurrency daily mean return time series linearity dynamics during the Covid-19 period. These cryptocurrencies were chosen based on their influence on the market, primarily driven by its market capitalisation. Tether is included as the most important stable coin on the market, nominally pegged to the U.S. dollar (USD). The reason to investigate it is that there are some inconsistencies in its behaviour as opposed to the other four cryptocurrencies. This study found that the behaviour of Tether cryptocurrency daily average return time series pattern is highly nonlinear and chaotic in nature, whereas the other four cryptocurrencies (namely Bitcoin, Ethereum, XRP and Bitcoin Cash) daily average return time series were found to be linear in nature. To further study Tether’s nonlinear time series rich dynamics, this study deployed one category of the regime switching models popularly known as the threshold regressions. The study estimates fairly suggest that both the threshold autoregression (TAR) and smooth transition autoregressive (STAR) models with lag 1 are adequate to capture the rich nonlinear and chaotic dynamics of Tether’s daily average return time series.

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Section: Literature Reviewmentioning

confidence: 99%

Dissecting Tether’s Nonlinear Dynamics during Covid-19

Maiti

Grubišić²,

Vuković

2020

Journal of Open Innovation: Technology, Market, and Complexity

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“…The Gaussian copula is the simplest of these models and has a restrictive dependence structure, i.e., its bivariate distribution can only be asymptotically independent or perfectly dependent, and its tail dependence structure is regulated by a single parameter: the correlation coefficient. Inverted max-stable models present the same difficulties for inference as max-stable models since often only likelihoods based on lower-dimensional densities are available (Padoan et al, 2010;Castruccio et al, 2016); the Huser-Wadsworth model, as well as its extension to model dependence jointly in the lower and upper tails (Gong and Huser, 2021), can capture both asymptotic dependence and independence but its distribution and (potentially censored) density functions rely on unidimensional integrals which have to be computed numerically, and this is computationally prohibitive in high dimensions, especially when computation of the multivariate normal distribution function is required; the conditional extremes model allows the change of asymptotic dependence class with distance between sites but it lacks a simple unconditional interpretation; see Huser and Wadsworth (2020) for a more detailed discussion.…”

Section: Introductionmentioning

confidence: 99%

Modeling spatial extremes using normal mean-variance mixtures

et al. 2022

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Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail decays at the same rate as the marginal tail. However, recent environmental data applications suggest that asymptotic independence is equally important and, unfortunately, existing spatial models in this setting that are both flexible and can be fitted efficiently are scarce. Here, we propose a new spatial copula model based on the generalized hyperbolic distribution, which is a specific normal mean-variance mixture and is very popular in financial modeling. The tail properties of this distribution have been studied in the literature, but with contradictory results. It turns out that the proofs from the literature contain mistakes. We here give a corrected theoretical description of its tail dependence structure and then exploit the model to analyze a simulated dataset from the inverted Brown-Resnick process, hindcast significant wave height data in the North Sea, and wind gust data in the state of Okla-

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“…To capture complex extremal dependence structure in multivariate spatial extremes, we propose in this paper a novel multi-factor copula model for multivariate spatial data that can capture all possible distinct combinations of extremal dependence types within each individual spatial process while allowing for flexible cross-process extremal dependence structures, for both the upper and lower tails. Our new model builds upon Huser and Wadsworth (2019), who proposed a spatial extremes model for the upper tail of a single variable, and it extends the bivariate copula model of Gong and Huser (2022), used to estimate time-varying tail dependencies in bivariate financial time series, to the multivariate spatial extremes setting. Rewriting our proposed model as a Bayesian hierarchical model with multiple latent variables, we here perform Bayesian inference using a customized Markov chain Monte Carlo (MCMC) algorithm based on carefully designed block proposals with an adaptive step size.…”

Section: Introductionmentioning

confidence: 99%

Flexible Modeling of Multivariate Spatial Extremes

Gong¹,

Huser²

2022

Preprint

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We develop a novel multi-factor copula model for multivariate spatial extremes, which is designed to capture the different combinations of marginal and cross-extremal dependence structures within and across different spatial random fields. Our proposed model, which can be seen as a multi-factor copula model, can capture all possible distinct combinations of extremal dependence structures within each individual spatial process while allowing flexible cross-process extremal dependence structures for both upper and lower tails. We show how to perform Bayesian inference for the proposed model using a Markov chain Monte Carlo algorithm based on carefully designed block proposals with an adaptive step size. In our real data application, we apply our model to study the upper and lower extremal dependence structures of the daily maximum air temperature (TMAX) and daily minimum air temperature (TMIN) from the state of Alabama in the southeastern United States. The fitted multivariate spatial model is found to provide a good fit in the lower and upper joint tails, both in terms of the spatial dependence structure within each individual process, as well as in terms of the cross-process dependence structure. Our results suggest that the TMAX and TMIN processes are quite strongly spatially dependent over the state of Alabama, and moderately cross-dependent.From a practical perspective, this implies that it may be worthwhile to model them jointly when interest lies in a computing spatial risk measures that involve both quantities.

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Asymmetric tail dependence modeling, with application to cryptocurrency market data

Cited by 15 publications

References 48 publications

Dissecting Tether’s Nonlinear Dynamics during Covid-19

Dissecting Tether’s Nonlinear Dynamics during Covid-19

Modeling spatial extremes using normal mean-variance mixtures

Flexible Modeling of Multivariate Spatial Extremes

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