Copulas for Markovian dependence

Details Copulas for Markovian dependence Copulas for Markovian dependence

2008-12-13

arxiv.org/abs/0812.2548v2

Bernoulli 2010, Vol. 16, No. 2, 331-342

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/09-BEJ214 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ214

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.

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