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Noncausality and Marginalization of Markov Processes

Author

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

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.

Suggested Citation

  • Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(2), pages 241-262, April.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:02:p:241-262_00
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    Citations

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    Cited by:

    1. Renault, Eric & Triacca, Umberto, 2015. "Causality and separability," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 1-5.
    2. Michel Mouchart & Renzo Orsi, 2016. "Building a Structural Model: Parameterization and Structurality," Econometrics, MDPI, vol. 4(2), pages 1-16, April.
    3. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
    4. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
    5. Jean-Pierre Florens & Denis Fougère & Thierry Kamionka & Michel Mouchart, 1994. "La modélisation économétrique des transitions individuelles sur le marché du travail," Économie et Prévision, Programme National Persée, vol. 116(5), pages 181-217.
    6. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    7. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    8. Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    9. Petrović, Ljiljana & Dimitrijević, Sladjana, 2012. "Causality with finite horizon of the past in continuous time," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1219-1223.
    10. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    11. MOUCHART, Michel & SAN MARTIN , Ernesto, 1998. "Identification problems in a class of mixture models with an application to the LISREL model," LIDAM Discussion Papers CORE 1998025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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