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COPULA-BASED CHARACTERIZATIONS FOR HIGHERORDER MARKOV PROCESSES
Published online by Cambridge University Press: 01 June 2009
Abstract
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In this paper, we obtain characterizations of higherorder Markov processes in terms of copulascorresponding to their finite-dimensionaldistributions. The results are applied to establishnecessary and sufficient conditions for Markovprocesses of a given order to exhibitm-dependence,r-independence, or conditionalsymmetry. The paper also presents a study ofapplicability and limitations of different copulafamilies in constructing higher order Markovprocesses with the preceding dependence properties.We further introduce new classes of copulas thatallow one to combine Markovness withm-dependence orr-independence in timeseries.
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Footnotes
This paper was previously circulated under thetitle “Copula-Based Dependence Characterizationsand Modeling for Time Series." An extended workingpaper version of the paper is available asIbragimov, 2005, “Copula-Based DependenceCharacterizations and Modeling for Time Series,”Harvard Institute of Economic Research Discussionpaper 2094. I thank three referees, DonaldAndrews, Brendan Beare, Christian Gourieroux,George Lentzas, Jeremiah Lowin, Andrew Patton,Peter Phillips, Murray Rosenblatt, YildirayYildirim, and the participants at seminars at theDepartments of Economics at Boston University,Harvard University, and Yale University, WhitmanSchool of Management at Syracuse University, andthe Harvard Statistics Summer Retreat on RecentAdvances in Computational Finance (June 2006) forhelpful comments and suggestions. A part of thepaper was completed under financial support from aYale University Dissertation Fellowship and aCowles Foundation Prize.
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