Class Of Multivariate Copulas Research Articles

Vine Copula Based Modeling

With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical (including the Gaussian and t-copula) and Archimedean families (such as Clayton and Gumbel copulas). Both classes are rather restrictive with regard to symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by building a multivariate model using only bivariate building blocks. This gives rise to highly flexible models that still allow for computationally tractable estimation and model selection procedures. These features made vine copula models quite popular among applied researchers in numerous areas of science. This article reviews the basic ideas underlying these models, presents estimation and model selection approaches, and discusses current developments and future directions.

Dynamics of HDI Index: Temporal Dependence Based on D-vine Copulas Model for Three-Way Data

The HDI (Human Development Index) is a widely used index based on the average of measures of health, education, and income. It assesses the progress of countries worldwide. The publicly available data set associated with the HDI can be seen as a table with 3 dimensions (three-way table): countries, indexes regarding progress, and years (from 2010 to 2018). Thus, modeling the serial dependence structure of this type of intricate three-way tables is a challenge. D-vine copulas are a special class of multivariate copulas that are particularly suited for modeling serial dependence. This work aims to assess the evolution of the dependence relationship between the indexes of the HDI data set over time through D-vine copulas, which has not been fully used before in the area, as far as we are concerned. We tested our approach to European and African countries and compare their results.

Some of the Most Common Copulas for Simulating Complex Survival Data

Simulation studies play an important role in the evaluation of the performance of avariety of statistical methods. Such assessment isperformed under computer intensive proceduresand cannot be achieved with studies of real dataalone. These studies are increasingly employed inevaluating the properties of the proposed methods being the generation of data the most fundamental and important component. However,only a few of published studies provide sufficientdetails to allow readers to understand fully allthe processes to generate the data. In this paperwe present a collection of practical algorithms forsimulating multivariate data from a wide class ofmultivariate copulas. This paper also details important considerations necessary when generating the survival data in a variety of scenarios. Asoftware application for R was developed in whichwe implement all the methods.

On the Structure of the Classes of Copulas and Quasi-Copulas with a Given Diagonal Section

In this paper we provide an alternative proof to that given in Ref. 1 to the fact that the class of multivariate copulas with a given diagonal section δ — denoted by 𝒞δ — is a singleton if, and only if, the unique element of the class is the copula of comonotonicity among random variables. This will be used to prove that, for any diagonal δ different from the diagonal of the comotonic copula, 𝒞δ is strictly included in the class of all multivariate quasi-copulas whose diagonal section is δ.

COMPOSITE BERNSTEIN COPULAS

AbstractCopula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.

Some Results on Convexity and Concavity of Multivariate Copulas

This paper provides some results on dierent types of con- vexity and concavity in the class of multivariate copulas. We also study their properties and provide several examples to illustrate our results.