Noncausality and Marginalization of Markov-processes

Florens, JP.;Mouchart, Michel;Rolin, Jean-Marie
(1993) Econometric Theory — Vol. 9, n° 2, p. 241-262 (1993)

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Authors
  • Florens, JP.
    Author
  • Mouchart, MichelUCLouvain
    Author
  • Rolin, Jean-MarieUCLouvain
    Author
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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Florens, JP., Mouchart, M., & Rolin, J.-M. (1993). Noncausality and Marginalization of Markov-processes. Econometric Theory, 9(2), 241-262. https://doi.org/10.1017/S0266466600007520 (Original work published 1993)