On dependence structure of copula-based Markov chains

Martial Longla

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 570-583
  • ISSN: 1292-8100

Abstract

top
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.

How to cite

top

Longla, Martial. "On dependence structure of copula-based Markov chains." ESAIM: Probability and Statistics 18 (2014): 570-583. <http://eudml.org/doc/274384>.

@article{Longla2014,
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.},
author = {Longla, Martial},
journal = {ESAIM: Probability and Statistics},
keywords = {Markov chains; copula; mixing; reversible processes; ergodicity; small sets; copulas},
language = {eng},
pages = {570-583},
publisher = {EDP-Sciences},
title = {On dependence structure of copula-based Markov chains},
url = {http://eudml.org/doc/274384},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Longla, Martial
TI - On dependence structure of copula-based Markov chains
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 570
EP - 583
AB - 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.
LA - eng
KW - Markov chains; copula; mixing; reversible processes; ergodicity; small sets; copulas
UR - http://eudml.org/doc/274384
ER -

References

top
  1. [1] B.K. Beare, Archimedean copulas and temporal dependence. Econ. Theory28 (2012) 1165–1185. Zbl1281.62143MR2998469
  2. [2] B.K. Beare, Copulas and Temporal Dependence. Econometrica78 (2010) 395–410. Zbl1202.91271MR2642867
  3. [3] R.C. Bradley, Introduction to strong mixing conditions. Vol. 1, 2. Kendrick press (2007). Zbl1134.60004MR2325294
  4. [4] K. Chan and H. Tong, Chaos: A Statistical Perspective. Springer, New York (2001). Zbl0977.62002MR1851668
  5. [5] P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes. Ann. Inst. Henri Poincaré, Section B, Tome 30 (1994) 63–82. Zbl0790.60037MR1262892
  6. [6] M. Longla and M. Peligrad, Some Aspects of Modeling Dependence in Copula-based Markov chains. J. Multiv. Anal.111 (2012) 234–240. Zbl1301.60089MR2944418
  7. [7] M. Longla, Remarks on the speed of convergence of mixing coefficients and applications. Stat. Probab. Lett.82 (2013) 2439–2445. Zbl1308.60086MR3093836
  8. [8] R.B. Nelsen, An introduction to copulas. 2nd edition. Springer, New York (2006). Zbl0909.62052MR2197664

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.