IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v76y2013i7p873-885.html
   My bibliography  Save this article

Monotone dependence in graphical models for multivariate Markov chains

Author

Listed:
  • Roberto Colombi
  • Sabrina Giordano

Abstract

We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according to the graph terminology—is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metrik:v:76:y:2013:i:7:p:873-885
    DOI: 10.1007/s00184-012-0421-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-012-0421-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00184-012-0421-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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, March.
    2. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    3. Chamberlain, Gary, 1982. "The General Equivalence of Granger and Sims Causality," Econometrica, Econometric Society, vol. 50(3), pages 569-581, May.
    4. Anna Gottard, 2007. "On the inclusion of bivariate marked point processes in graphical models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 269-287, November.
    5. Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
    6. Steen A. Andersson & David Madigan & Michael D. Perlman, 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, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    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.
    3. Eichler, M. & Didelez, V., 2009. "On Granger-causality and the effect of interventions in time series," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Loperfido, Nicola, 2010. "A note on marginal and conditional independence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1695-1699, December.
    5. Robin J. Evans & Thomas S. Richardson, 2013. "Marginal log-linear parameters for graphical Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 743-768, September.
    6. Chen, Pu & Hsiao, Chih-Ying, 2010. "Looking behind Granger causality," MPRA Paper 24859, University Library of Munich, Germany.
    7. Ralf Brüggemann & Christian Kascha, 2017. "Directed Graphs and Variable Selection in Large Vector Autoregressive Models," Working Paper Series of the Department of Economics, University of Konstanz 2017-06, Department of Economics, University of Konstanz.
    8. Admasu A. Maruta & Habtamu T. Edjigu & Woubet Kassa, 2023. "Does financial inclusion empower women in Africa?," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 52(3), November.
    9. Maria Blangiewicz & Krystyna Strzala, 2008. "Notes on a Forecasting Procedure," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 75-84.
    10. Danau, Daniel, 2020. "Prudence and preference for flexibility gain," European Journal of Operational Research, Elsevier, vol. 287(2), pages 776-785.
    11. Tan T. M. Le & Franck Martin & Duc K. Nguyen, 2018. "Dynamic connectedness of global currencies: a conditional Granger-causality approach," Economics Working Paper Archive (University of Rennes & University of Caen) 2018-04, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    12. Upadhyay, Shashankaditya & Banerjee, Anirban & Panigrahi, Prasanta K., 2020. "Causal evolution of global crisis in financial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    13. Didier Sornette & Wei-Xing Zhou, 2005. "Non-parametric determination of real-time lag structure between two time series: the 'optimal thermal causal path' method," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 577-591.
    14. Lorenza Rossi & Emilio Zanetti Chini, 2016. "Firms’ Dynamics and Business Cycle: New Disaggregated Data," DEM Working Papers Series 123, University of Pavia, Department of Economics and Management.
    15. Teye, Alfred Larm & Ahelegbey, Daniel Felix, 2017. "Detecting spatial and temporal house price diffusion in the Netherlands: A Bayesian network approach," Regional Science and Urban Economics, Elsevier, vol. 65(C), pages 56-64.
    16. Chen, Pu & Chihying, Hsiao, 2007. "Learning Causal Relations in Multivariate Time Series Data," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 1, pages 1-43.
    17. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    18. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    19. Rigana, Katerina & Wit, Ernst-Jan Camiel & Cook, Samantha, 2023. "A new way of measuring effects of financial crisis on contagion in currency markets," International Review of Financial Analysis, Elsevier, vol. 90(C).
    20. Xiandeng Jiang & Le Chang & Yanlin Shi, 2023. "Housing price diffusions in mainland China: evidence from a spatially penalized graphical VAR model," Empirical Economics, Springer, vol. 64(2), pages 765-795, February.

    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:spr:metrik:v:76:y:2013:i:7:p:873-885. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.