2017/05/30 by Mohamad A. Khaled, Robert Kohn, Khaled, Mohamad A. +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Probability and Statistical Research
paper · pdf · doi:10.48550/arxiv.1705.10440
openalex publication_date 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Copulas are now frequently used to construct or estimate multivariate distributions because of their ability to take into account the multivariate dependence of the different variables while separately specifying marginal distributions. Copula based multivariate models can often also be more parsimonious than fitting a flexible multivariate model, such as a mixture of normals model, directly to the data. However, to be effective, it is imperative that the family of copula models considered is sufficiently flexible. Although finite mixtures of copulas have been used to construct flexible families of copulas, their approximation properties are not well understood and we show that natural candidates such as mixtures of elliptical copulas and mixtures of Archimedean copulas cannot approximate a general copula arbitrarily well. Our article develops fundamental tools for approximating a general copula arbitrarily well by a copulas based on finite mixtures. We show the asymptotic properties as well as illustrate the advantages of our methodology empirically on a financial data set and on some artificial data.