IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v107y2012icp90-103.html
   My bibliography  Save this article

Graphical models for multivariate Markov chains

Author

Listed:
  • Colombi, R.
  • Giordano, S.

Abstract

The aim of this paper is to provide a graphical representation of the dynamic relations among the marginal processes of a first order multivariate Markov chain. We show how to read Granger-noncausal and contemporaneous independence relations off a particular type of mixed graph, when directed and bi-directed edges are missing. Insights are also provided into the Markov properties with respect to a graph that are retained under marginalization of a multivariate chain. Multivariate logistic models for transition probabilities are associated with the mixed graphs encoding the relevant independencies. Finally, an application on real data illustrates the methodology.

Suggested Citation

  • Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
  • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:90-103
    DOI: 10.1016/j.jmva.2012.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000115
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bouissou, Michel B & Laffont, Jean-Jacques & Vuong, Quang H, 1986. "Tests of Noncausality under Markov Assumptions for Qualitative Panel Data," Econometrica, Econometric Society, vol. 54(2), pages 395-414, March.
    2. Thomas Richardson, 2003. "Markov Properties for Acyclic Directed Mixed Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 145-157.
    3. Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
    4. Joseph B. Lang, 2005. "Homogeneous Linear Predictor Models for Contingency Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 121-134, March.
    5. Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(02), pages 241-262, April.
    6. Christian Gouriéroux & Alain Monfort & Eric Renault, 1987. "Kullback Causality Measures," Annals of Economics and Statistics, GENES, issue 6-7, pages 369-410.
    7. Chamberlain, Gary, 1982. "The General Equivalence of Granger and Sims Causality," Econometrica, Econometric Society, vol. 50(3), pages 569-581, May.
    8. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    9. Monia Lupparelli & Giovanni M. Marchetti & Wicher P. Bergsma, 2009. "Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 559-576.
    10. repec:adr:anecst:y:1987:i:6-7 is not listed on IDEAS
    11. Steen A. Andersson, 2001. "Alternative Markov Properties for Chain Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 33-85.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roberto Colombi & Sabrina Giordano, 2013. "Monotone dependence in graphical models for multivariate Markov chains," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 873-885, October.
    2. Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:90-103. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.