First order autoregressive representation of Markov bi-dimensional chains of 1-order

Authors

  • M BOUSSEBOUA Université Constantine 1
  • F. L RAHMANI Université Constantine 1

Keywords:

Markov’chains, autoregressive process, spectral density, diagonal development of bivariate distribution

Abstract

This paper suggests an extension of Lai’s results about the first order autoregressive
representation of Markov bi-dimensional chain of 1-order. In the case of markov chain with
independent components, we find of course the conditions validating these results for each
component.

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Author Biographies

M BOUSSEBOUA, Université Constantine 1

Département de Mathématique

F. L RAHMANI, Université Constantine 1

Département de Mathématique

References

Brockwell, P. J. and Davis R. A., (1987). Time series :

Theory and methods (Springer Verlag).

Feller, W., (1968). An introduction to probability theory

and its application Vol 1 (John Wiley & sons)

Fuller, W.A. (1996). Introduction to Statistical Times

series (Wiley Series in Probability and statistics).

Lai, C.D.,(1977). First order autoregressive markov

processes. Stochastic processes and their applications, 3

-4.

Lancaster, P., (1968.). Theory of matrices (Academic

Press).

Published

2006-12-01

How to Cite

BOUSSEBOUA, M., & RAHMANI, F. L. (2006). First order autoregressive representation of Markov bi-dimensional chains of 1-order. Sciences & Technology. A, Exactes Sciences, (24), 36–40. Retrieved from https://revue.umc.edu.dz/a/article/view/150

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