Tails of correlation mixtures of elliptical copulas

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is generally larger than in the limit, which can have serious consequences for estimation and evaluation of extreme risk. Finally, although correlation mixtures of Gaussian copulas inherit the property of asymptotic independence, at the same time they fall in the newly defined category of near asymptotic dependence. The consequences of these findings for modeling are assessed by means of a simulation study and a case study involving financial time series.Comment: 21 pages, 3 figure

Factor copula models for item response data

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data

Are benefits from oil - stocks diversification gone? New evidence from a dynamic copula and high frequency data

Oil is perceived as a good diversification tool for stock markets. To fully understand this potential, we propose a new empirical methodology that combines generalized autoregressive score copula functions with high frequency data and allows us to capture and forecast the conditional time-varying joint distribution of the oil -- stocks pair accurately. Our realized GARCH with time-varying copula yields statistically better forecasts of the dependence and quantiles of the distribution relative to competing models. Employing a recently proposed conditional diversification benefits measure that considers higher-order moments and nonlinear dependence from tail events, we document decreasing benefits from diversification over the past ten years. The diversification benefits implied by our empirical model are, moreover, strongly varied over time. These findings have important implications for asset allocation, as the benefits of including oil in stock portfolios may not be as large as perceived

Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment