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Noncausality and Marginalization of Markov Processes

Published online by Cambridge University Press:  11 February 2009

J.P. Florens,
M. Mouchart and
J.M. Rolin
J.P. Florens
Affiliation:
Université des Sciences Sociales
M. Mouchart
Affiliation:
Université Catholique de Louvain
J.M. Rolin
Affiliation:
Université Catholique de Louvain
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Abstract

In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both finite and infinite noncausality only if it is markovian. Counterexamples are also given to illustrate the cases where these further conditions are not satisfied.

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Type
Articles
Information
Econometric Theory , Volume 9 , Issue 2 , April 1993, pp. 241 - 262
Copyright
Copyright © Cambridge University Press 1993

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