New copula families and mixing properties

We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula famil...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2024-09, Vol.65 (7), p.4331-4363
Main Author: Longla, Martial
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Markov analysis
Markov chains
Mathematics and Statistics
Operations Research/Decision Theory
Parameter estimation
Probability Theory and Stochastic Processes
Regular Article
Statistics
Statistics for Business
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Summary:We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate ψ -mixing Markov chains. Some general results on ψ -mixing are given. The Spearman’s correlation ρ S and Kendall’s τ are provided for the created copula families. Some general remarks are provided for ρ S and τ . A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-024-01559-9