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Product autoregression: a time-series characterization of the gamma distribution

Published online by Cambridge University Press:  14 July 2016

Ed Mckenzie
Ed Mckenzie*
Affiliation:
University of Strathclyde
*
∗ Postal address: Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond St, Glasgow G1 1XH, U.K.
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Abstract

A non-linear stationary stochastic process {Xt} is derived and shown to have the property that both the processes {Xt} and {log Xt} have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.

Keywords

NON-LINEAR AUTOREGRESSIONSELF-DECOMPOSABILITYLOGARITHMIC TRANSFORMATIONGAMMA DISTRIBUTION CHARACTERIZATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 463 - 468
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This paper presents material on which was based a talk of the same title given at the 13th European Meeting of Statisticians, held in Brighton in September 1980.

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