Copulas for Markovian dependence
Abstract
Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some difficulties with using copulas even for Markov processes: some tractable copulas such as mixtures between copulas of complete co- and countermonotonicity and independence (Fr\'{e}chet copulas) are shown to imply quite a restricted type of Markov process and Archimedean copulas are shown to be incompatible with Markov chains. We also investigate Markov chains that are spreadable or, equivalently, conditionally i.i.d.
Cite
@article{arxiv.0812.2548,
title = {Copulas for Markovian dependence},
author = {Andreas N. Lagerås},
journal= {arXiv preprint arXiv:0812.2548},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.3150/09-BEJ214 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)