Author:
Yeh Hsiaw-Chan,Arnold Barry C.,Robertson Christopher A.
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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference8 articles.
1. On Extreme Order Statistics
2. The exponential autoregressive-moving average EARMA(p, q) process;Lawrance;J.R. Statist. Soc.,1980
3. A Rapidly Convergent Descent Method for Minimization
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