Local dependence estimation using semiparametric archimedean copulas

The authors define a new semiparametric Archimedean copula family which has a flexible dependence structure. The generator of the family is a local interpolation of existing generators. It has locally‐defined dependence parameters. The authors present a penalized constrained least‐squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bi‐variate survival example.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

On the preservation of copula structure under truncation

The author characterizes the copula associated with the bivariate survival model of Clayton (1978) as the only absolutely continuous copula that is preserved under bivariate truncation.     

Moment‐Independent Sensitivity Analysis Using Copula

In risk assessment, the moment‐independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire distribution range of model output. In this article, along the lines of Plischke et al., we point out that the original moment‐independent SA index (also called delta index) can also be interpreted as the dependence measure between model output and input variables, and introduce another moment‐independent SA index (called extended delta index) based on copula. Then, nonparametric methods for estimating the delta and extended delta indices are proposed. Both methods need only a set of samples to compute all the indices; thus, they conquer the problem of the “curse of dimensionality.” At last, an analytical test example, a risk assessment model, and the levelE model are employed for comparing the delta and the extended delta indices and testing the two calculation methods. Results show that the delta and the extended delta indices produce the same importance ranking in these three test examples. It is also shown that these two proposed calculation methods dramatically reduce the computational burden.     

Semi-polynomial copulas

In this paper, we characterise a family of bivariate copulas whose sections between the main diagonal and the border of the unit square are polynomial, generalising several families of copulas, including those with quadratic and cubic sections. We also study a measure of association and the tail dependence for this class, illustrating our results with several examples.     

Fitting competing risks data to bivariate Pareto models

This paper revisits two bivariate Pareto models for fitting competing risks data. The first model is the Frank copula model, and the second one is a bivariate Pareto model introduced by Sankaran and Nair (1993 Sankaran, P. G., and N. U. Nair. 1993. A bivariate Pareto model and its applications to reliability. Naval Research Logistics 40 (7):1013–1020. doi:10.1002/1520-6750(199312)40:7%3c1013::AID-NAV3220400711%3e3.0.CO;2-7.[Crossref], [Web of Science ®] , [Google Scholar]). We discuss the identifiability issues of these models and develop the maximum likelihood estimation procedures including their computational algorithms and model-diagnostic procedures. Simulations are conducted to examine the performance of the maximum likelihood estimation. Real data are analyzed for illustration.     

Generalized information matrix tests for copulas

We propose a family of goodness-of-fit tests for copulas. The tests use generalizations of the information matrix (IM) equality of White and so relate to the copula test proposed by Huang and Prokhorov. The idea is that eigenspectrum-based statements of the IM equality reduce the degrees of freedom of the test’s asymptotic distribution and lead to better size-power properties, even in high dimensions. The gains are especially pronounced for vine copulas, where additional benefits come from simplifications of score functions and the Hessian. We derive the asymptotic distribution of the generalized tests, accounting for the nonparametric estimation of the marginals and apply a parametric bootstrap procedure, valid when asymptotic critical values are inaccurate. In Monte Carlo simulations, we study the behavior of the new tests, compare them with several Cramer–von Mises type tests and confirm the desired properties of the new tests in high dimensions.     

基于动态因子Copula模型的行业间系统性风险分析

国际金融市场间的相关关系以及系统性风险受到很多学者的重视，本文则以我国股市的行业指数作为研究对象进行实证研究。通过构建动态因子Copula模型，文章对行业的日收益率数据进行了动态相关性分析，并基于风险预期占比度量了我国行业之间系统性风险的溢出效应。本文分析了2006年1月4日至2016年7月1日的28个行业指数数据，基于GAS动态负荷因子的变化路径来刻画其相关关系，通过风险预期占比来研究行业间的风险溢出效应。研究表明，各个行业指数收益率之间存在较强的关联性。就单个行业来说，化工行业与其他行业关系最为不稳定。就金融与非金融行业而言，金融行业对非金融行业的影响较大且较为平稳。本文所得研究结果可以为投资者和风险管理者在进行决策时提供一定的指导。