Abstract
This paper introduces a new parametric copula family based on Fourier expansions and flexible enough to describe arbitrary structures. We derive its various properties and show that it can be fit efficiently by the Fast Fourier Transform. We overcome the Fourier series' assumption of periodicity by using a pseudo-copula and demonstrate the resulting model's superiority in applications like financial risk management. The concept of discordant tail dependence is introduced along with a Fourier-Clayton mixture copula. The Fourier-Clayton copula allows for some measure of tail and also reduces the dimensionality of the Fourier copula's parameter space. The distinguishing feature of this new family of copulas is its ability to transform a flexible nonparametric density estimate into a robust parametric model.(A version of this paper was awarded the Thomas T. Hoopes Prize by Harvard University and the Allyn A. Young Prize by the Harvard University Department of Economics.)
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