On tail dependence : a characterization for first-order max-autoregressive processes.

Abstract

In this paper, we consider first-orderMARMAorARMAXprocesses and amodified version of these involving a power transformation, denoted pARMAX.We assume Pareto-type tails, the most interesting case for inference within these processes. Some well-known dependencemeasures of multivariate extreme value theory are considered in a time series framework. In calculating these measures, we find that ARMAX and pARMAX have opposite behavior in concomitant extremes, covering all types of tail dependence. This characterization will serve modeling purposes.