Abstract
Abstract This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.
Highlights
Copulas are attractive tools to model multivariate dependence structures in a exible way
This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]
This paper proposes Bayesian methods to estimate generalized partition of unity copulas (GPUCs)
Summary
Copulas are attractive tools to model multivariate dependence structures in a exible way. They are widely applied in elds where it is crucial to have a good working model of the joint distribution, e.g. in nance or portfolio management. The simplest way is, the empirical copula Another nonparametric copula is the Bernstein copula [1] which builds on Bernstein polynomials to smooth the estimated copula density. [18] and [15] developed a more general family of nonparametric copulas, the so called Generalized Partition of Unity Copulas (GPUC).
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