Pareto processes

Abstract

An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), 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 (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.

A Gini Autocovariance Function for Time Series Modelling

“…Here, we examine the Gini ACV for a nonlinear type of AR process with possibly infinite variance. Yeh et al (1988) introduce, in different notation, a nonlinear AR Pareto process YARP(III)(1) given by…”

“…Under second-order assumptions (˛> 2), the usual ACV is defined but problematic. Yeh et al (1988) give an explicit formula for .0/ but only an implicit formula involving an incomplete beta integral for .1/ and do not treat .k/, k 2. Therefore, alternative approaches have been developed to explore quantitatively the dependence features of YARP(III)(1).…”

Tail Dependence of a Pareto Process

“…We consider autoregressive Pareto(III) processes, more precisely, the Yeh-Arnold-Robertson Pareto(III) [12], in short YARP(III)(1), given by…”

Mathematical Modelling on Lamprey GnRH-III using Autoregressive Logistic Processes

“…Since the LH has shown a fairly steady downward trend against the FSH. (in figure 2.1 ) These transformations will fit in a power-logistic process [9].…”