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

In this paper, we consider first-order MARMA or ARMAX processes and a modified 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 dependence measures 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.