Hidden Regular Variation under Full and Strong Asymptotic Dependence

Data exhibiting heavy-tails in one or more dimensions is often studied using the paradigm of regular variation. In a multivariate setting this often leads to observing specific forms of dependence in the data; this means data tends to concentrate along particular directions and does not cover the full space. This is observed in various data sets in finance, insurance, network traffic, etc. In this paper we discuss the notions of asymptotic full dependence and asymptotic strong dependence for bivariate data {along with the idea of hidden regular variation in these cases}. Analyses of two data sets illustrate each concept.