A class of bivariate integer-valued time series models was constructed via copula theory. Each follows a Markov chain with the serial dependence captured using copula-based transition probabilities from Poisson and zero-inflated (ZIP) margins. The theory also used again to capture between two either Gaussian or “t-copula” functions. Such method provides flexible structure that allows for positi...

Dependence modelling plays a crucial role within internal credit risk models. The theory of copulae, which describes the dependence structure between a multi-dimensional distribution function and the corresponding marginal distributions, provides useful tools for dependence modelling. The difficulty in employing copulae for internal credit risk models arises from the appropriate choice of a cop...

One of the biggest advances in recent years for high-dimensional copula models and applications has been the development of the vine pair-copula construction that covers continuous and discrete variables, and its extensions to include latent variables. Software has been made available in the VineCopula R package and the package that is companion to the book by Joe [6]. This special issue of the...

‎One of the most useful tools for handling multivariate distributions of dependent variables in terms of their marginal distribution is a copula function‎. ‎The copula families capture a fair amount of attention due to their applicability and flexibility in describing the non-Gaussian spatial dependent data‎. ‎The particular properties of the spatial copula are rarely ...

In this paper, we consider different issues related to Archimedean copulae and positive dependence. In the first part, we characterize Archimedean copulae that possess positive dependence properties such as multivariate total positivity of order 2 ðMTP2Þ and conditionally increasingness in sequence. In the second part, we investigate conditions for exchangeable binary sequences to admit an Arch...

In mathematical finance and other applications of statistics, the computation of expectations is often taken over a multi-dimensional probability distribution where there is no clear multivariate distribution. Copula theory has become increasingly popular as a means of gluing marginals together to circumvent this difficulty. There is then the issue of reconciling the distributions implied by va...

When I started writing the paper [19] in 2003 a Google search of the word “copula” gave 10,000 responses. In September 2005 the same search gives 650,000 responses. There is an explosion of activity. What is going on? Many of the web-sites found in the Google search are related to mathematical finance, statistics, extreme value theory, and risk management. Everybody who opens any journal on sto...

The famous Sklar’s theorem (see [54]) allows to build multivariate distributions using a copula and marginal distributions. For the basic theory on copulas see the first chapter ([14]) or the books on copulas by Joe ([32]) and Nelson ([51]). Much emphasis has been put on the bivariate case and in [32] and [51] many examples of bivariate copula families are given. However the class of multivaria...

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In thi...