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A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)

Published online by Cambridge University Press:  01 July 2016

P. A. Jacobs  and
P. A. W. Lewis
P. A. Jacobs
Affiliation:
Stanford University
P. A. W. Lewis
Affiliation:
Naval Postgraduate School, Monterey, California
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Abstract

A stationary sequence of random variables with exponential marginal distributions and the correlation structure of an ARMA (1, 1) process is defined. The process is formed as a random linear combination of i.i.d. exponential random variables and is very simple to generate on a computer. Moments and joint distributions for the sequence are obtained, as well as limiting properties of sums of the random variables and of the point process whose intervals have the EARMA (1, 1) structure.

Keywords

POINT PROCESSEXPONENTIAL DISTRIBUTIONPROBABILISTIC LINEAR MODELMOVING AVERAGEAUTOREGRESSIVEVARIANCE-TIME CURVEPOISSON PROCESSDEPENDENT SEQUENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 1 , March 1977 , pp. 87 - 104
Copyright
Copyright © Applied Probability Trust 1977 

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