Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-16T07:01:53.268Z Has data issue: false hasContentIssue false
  • English
  • Français

On dependence structure of copula-based Markov chains

Published online by Cambridge University Press:  10 October 2014

Martial Longla
Martial Longla*
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, USA. longla_m_martial@yahoo.com; mlongla@olemiss.edu
Get access

Abstract

We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential ρ-mixing. We analyse the example of the Mardia and Frechet copula families using small sets.

Keywords

Markov chainscopulamixingreversible processesergodicitysmall sets
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 570 - 583
Copyright
© EDP Sciences, SMAI 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beare, B.K., Archimedean copulas and temporal dependence. Econ. Theory 28 (2012) 1165–1185. Google Scholar
Beare, B.K., Copulas and Temporal Dependence. Econometrica 78 (2010) 395–410. Google Scholar
R.C. Bradley, Introduction to strong mixing conditions. Vol. 1, 2. Kendrick press (2007).
K. Chan and H. Tong, Chaos: A Statistical Perspective. Springer, New York (2001).
Doukhan, P., Massart, P. and Rio, E., The functional central limit theorem for strongly mixing processes. Ann. Inst. Henri Poincaré, Section B, Tome 30 (1994) 63–82. Google Scholar
Longla, M. and Peligrad, M., Some Aspects of Modeling Dependence in Copula-based Markov chains. J. Multiv. Anal. 111 (2012) 234–240. Google Scholar
Longla, M., Remarks on the speed of convergence of mixing coefficients and applications. Stat. Probab. Lett. 82 (2013) 2439–2445. Google Scholar
R.B. Nelsen, An introduction to copulas. 2nd edition. Springer, New York (2006).