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An exponential moving-average sequence and point process (EMA1)

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance  and
P. A. W. Lewis
A. J. Lawrance
Affiliation:
University of Birmingham
P. A. W. Lewis
Affiliation:
Naval Postgraduate School, Monterey, California
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Abstract

A construction is given for a stationary sequence of random variables {Xi} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {εi}. The joint and trivariate exponential distributions of Xi−1, Xi and Xi+ 1 are studied, as well as the intensity function, point spectrum and variance time curve for the point process which has the {Xi} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higher-order moving averages and Gamma point processes are discussed.

Keywords

POINT PROCESSEXPONENTIAL INTERVALSCORRELATED EXPONENTIAL SEQUENCEMOVING AVERAGE STRUCTURESPECTRUM OF COUNTSBIVARIATE EXPONENTIAL DISTRIBUTIONCONDITIONAL CORRELATIONSTATIONARY INITIAL CONDITIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 98 - 113
Copyright
Copyright © Applied Probability Trust 1977 

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References

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