Copula measures and Sklar's theorem in arbitrary dimensions

Fred Espen Benth, Giulia Di Nunno and Dennis Schroers

Scandinavian Journal of Statistics, 2022, vol. 49, issue 3, 1144-1183

Abstract: Although copulas are used and defined for various infinite‐dimensional objects (e.g., Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified functional analytic framework, show how Sklar's theorem can be applied in certain examples of Banach spaces and provide a semiparametric estimation procedure for second‐order stochastic processes with underlying Gaussian copula.

Date: 2022
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https://doi.org/10.1111/sjos.12559

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