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Forward and reversed time prediction of autoregressive sequences

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Stamatis Cambanis  and
Issa Fakhre-Zakeri
Stamatis Cambanis*
Affiliation:
University of North Carolina
Issa Fakhre-Zakeri*
Affiliation:
University of North Carolina
*
†Professor Cambanis died on 12 April 1995. An obituary for him was recently published in this journal (J. Appl. Prob. 33, 284).
†Professor Cambanis died on 12 April 1995. An obituary for him was recently published in this journal (J. Appl. Prob. 33, 284).
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Abstract

Prediction for autoregressive sequences with finite second moment and of general order is considered. It is shown that the best predictor with time reversed is linear if and only if the innovations are Gaussian. The connection to time reversibility is also discussed.

Keywords

AUTOREGRESSIVE PROCESSESLINEAR PREDICTIONREGRESSIONSTABLE AND SEMISTABLE DISTRIBUTIONSTIME-REVERSIBILITY

MSC classification

Primary: 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc. 62M20: Prediction
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1053 - 1060
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL 03 92 G 0008.

References

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