Noncausality and Marginalization of Markov Processes

J.P. Florens, M. Mouchart and J.M. Rolin

Econometric Theory, 1993, vol. 9, issue 2, 241-262

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.

Date: 1993
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