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Time-reversibility of linear stochastic processes

Published online by Cambridge University Press:  14 July 2016

Gideon Weiss
Gideon Weiss*
Affiliation:
Tel-Aviv University
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Abstract

Time-reversibility is defined for a process X(t) as the property that {X(t1), …, X(tn)} and {X(– t1), …, X(– tn)} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.

Keywords

TIME-REVERSIBILITYSHOT NOISECHARACTERISATIONS OF THE NORMAL DISTRIBUTIONTIME SERIESSTOCHASTIC PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 831 - 836
Copyright
Copyright © Applied Probability Trust 1975 

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References

Bartlett, M. S. (1957) Contribution to discussion of papers by Dr. Gani and Mr. Kendall. J. R. Statist. Soc. B. 19, 220–221.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications. Vol. II, 2nd Ed., Wiley, New York.Google Scholar
Parzen, E. (1964) Stochastic Processes. Holden Day, San Francisco.Google Scholar
Rao, C. R. (1966) Characterisation of the distribution of random variables in linear structural relations. Sankhya A 28, 251–260.Google Scholar