Extremal Dependence Concepts

Modelling across extremal dependence classes

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for, but can substa...

Extremal Dependence: Internet Traffic Applications

For bivariate heavy tailed data, the extremes may carry distinctive dependence information not seen from moderate values. For example, a large value in one component may help cause a large value in the other. This is the idea behind the notion of extremal dependence. We discuss ways to detect and measure extremal dependence. We apply the techniques discussed to internet data and conclude that f...

On extremal dependence of block vectors

Extremal dependence of copulas: A tail density approach

The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze extremal dependence of the copulas that are specified only by densities. The relation between the cop...

Extremal (in)dependence of a Maximum Autoregressive Process

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended ...