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COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES

Published online by Cambridge University Press:  01 June 2009

Rustam Ibragimov
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Abstract

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibit m-dependence, r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness with m-dependence or r-independence in time series.

Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 819 - 846
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

This paper was previously circulated under the title “Copula-Based Dependence Characterizations and Modeling for Time Series." An extended working paper version of the paper is available as Ibragimov, 2005, “Copula-Based Dependence Characterizations and Modeling for Time Series,” Harvard Institute of Economic Research Discussion paper 2094. I thank three referees, Donald Andrews, Brendan Beare, Christian Gourieroux, George Lentzas, Jeremiah Lowin, Andrew Patton, Peter Phillips, Murray Rosenblatt, Yildiray Yildirim, and the participants at seminars at the Departments of Economics at Boston University, Harvard University, and Yale University, Whitman School of Management at Syracuse University, and the Harvard Statistics Summer Retreat on Recent Advances in Computational Finance (June 2006) for helpful comments and suggestions. A part of the paper was completed under financial support from a Yale University Dissertation Fellowship and a Cowles Foundation Prize.

References

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