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Bivariate exponential and geometric autoregressive and autoregressive moving average models

Published online by Cambridge University Press:  01 July 2016

H. W. Block ,
N. A. Langberg  and
D. S. Stoffer
H. W. Block*
Affiliation:
University of Pittsburgh
N. A. Langberg*
Affiliation:
University of Haifa
D. S. Stoffer*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
∗∗Postal address: Department of Statistics, University of Haifa, Mount Carmel, Haifa 31999, Israel.
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
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Abstract

We present autoregressive (AR) and autoregressive moving average (ARMA) processes with bivariate exponential (BE) and bivariate geometric (BG) distributions. The theory of positive dependence is used to show that in various cases, the BEAR, BGAR, BEARMA, and BGARMA models consist of associated random variables. We discuss special cases of the BEAR and BGAR processes in which the bivariate processes are stationary and have well-known bivariate exponential and geometric distributions. Finally, we fit a BEAR model to a real data set.

Keywords

BIVARIATE EXPONENTIAL AND GEOMETRIC DISTRIBUTIONSBIVARIATE AUTOREGRESSIVE AND AUTOREGRESSIVE MOVING AVERAGE MODELS IN EXPONENTIAL AND GEOMETRIC RANDOM VECTORSASSOCIATIONJOINT STATIONARITY
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 4 , December 1988 , pp. 798 - 821
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research partially supported by the Air Force Office of Scientific Research under Contract AFOSR-84–0113.

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