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Pareto processes

Published online by Cambridge University Press:  14 July 2016

Hsiaw-Chan Yeh ,
Barry C. Arnold  and
Christopher A. Robertson
Hsiaw-Chan Yeh*
Affiliation:
National Taiwan University
Barry C. Arnold*
Affiliation:
National Taiwan University
Christopher A. Robertson*
Affiliation:
University of California, Riverside
*
∗Postal address: Department of Finance, National Taiwan University, 21 Hsu-Chow Road, Taipei, Taiwan 10020, Republic of China.
∗∗Postal address: Department of Statistics, University of California, Riverside, CA 92521, USA.
∗∗Postal address: Department of Statistics, University of California, Riverside, CA 92521, USA.
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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.

Keywords

AUTOREGRESSIVE PROCESSBIVARIATE PARETO DISTRIBUTIONSEXTREMAL PROCESSESGEOMETRIC MINIMA
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 291 - 301
Copyright
Copyright © Applied Probability Trust 1988 

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References

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