Pareto processes

An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrence and Lewis, is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti. Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.