Time-reversibility of linear stochastic processes

Gideon Weiss

doi:10.2307/3212735

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.

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

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Weiss, Gideon and Westcott, Mark 1976. A note on identification, characterisation of the Gaussian distribution and time reversibility in linear stochastic processes. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 35, Issue. 2, p. 151.

Weiss, Gideon 1977. Shot noise models for the generation of synthetic streamflow data. Water Resources Research, Vol. 13, Issue. 1, p. 101.

Anderson, O.D. 1977. The time series concept of invertibility. Series Statistics, Vol. 8, Issue. 3, p. 399.

1985. Discussion of the Paper by Drs Lawrance and Lewis. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol. 47, Issue. 2, p. 183.

Lewis, P. A. W. 1985. SOME SIMPLE MODELS FOR CONTINUOUS VARIATE TIME SERIES1. JAWRA Journal of the American Water Resources Association, Vol. 21, Issue. 4, p. 635.

Dewald, L. and Lewis, P. 1985. A new Laplace second-order autoregressive time-series model--NLAR(2). IEEE Transactions on Information Theory, Vol. 31, Issue. 5, p. 645.

McKenzie, Ed. 1985. SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES1. JAWRA Journal of the American Water Resources Association, Vol. 21, Issue. 4, p. 645.

Fernandez, Bonifacio and Salas, Jose D. 1986. Periodic Gamma Autoregressive Processes for Operational Hydrology. Water Resources Research, Vol. 22, Issue. 10, p. 1385.

Johnson, D. and Rao, P.S. 1987. Properties and generation of non-Gaussian time series. p. 37.

Chernick, M. R. Daley, D. J. and Littlejohn, R. P. 1988. A time-reversibility relationship between two Markov chains with exponential stationary distributions. Journal of Applied Probability, Vol. 25, Issue. 02, p. 418.

McKenzie, ED 1988. The distributional structure of finite moving-average processes. Journal of Applied Probability, Vol. 25, Issue. 2, p. 313.

Rao, P.S. and Johnson, D.H. 1988. A first-order AR model for non-Gaussian time series. p. 1534.

Li, W. K. and McLeod, A. I. 1988. ARMA MODELLING WITH NON‐GAUSSIAN INNOVATIONS. Journal of Time Series Analysis, Vol. 9, Issue. 2, p. 155.

Mckenzie, Ed 1988. Some ARMA models for dependent sequences of poisson counts. Advances in Applied Probability, Vol. 20, Issue. 4, p. 822.

Hutchinson, M.F. 1990. A point rainfall model based on a three-state continuous Markov occurrence process. Journal of Hydrology, Vol. 114, Issue. 1-2, p. 125.

Johnson, D.H. and Rao, P.S. 1991. On the existence of Gaussian noise (signal modelling). p. 1673.

Swift, A. L. and Janacek, G. J. 1991. Forecasting non‐normal time series. Journal of Forecasting, Vol. 10, Issue. 5, p. 501.

Giannakis, G.B. and Tsatsanis, M.K. 1991. HOS or SOS for parametric modeling?. p. 3097.

Swami, A. and Mendel, J.M. 1991. Cumulant-based approach to harmonic retrieval and related problems. IEEE Transactions on Signal Processing, Vol. 39, Issue. 5, p. 1099.

Download full list

Article contents

Time-reversibility of linear stochastic processes

Abstract

Keywords

Access options

References

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Time-reversibility of linear stochastic processes

Abstract

Keywords

Access options

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests