This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented for selecting an appropriate model, estimating its parameters, and checking its goodness-of-fit. A larger, realistic application of the methodology to hydrological data is then presented.

http://quantlabs.net/academy/download/free_quant_instituitional_books_/%5BJournal%20of%20Hydrologic%20Engineering,%20Genest%5D%20Everything%20You%20Always%20Wanted%20to%20Know%20about%20Copula%20Modeling%20but%20Were%20Afraid%20to%20Ask.pdf

Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask

/pdf/chapter-8-modelling-dependence-with-copulas-and-applications-36v2unmor5.pdf

Chapter 8 – Modelling Dependence with Copulas and Applications to Risk Management

Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on "blanket tests", i.e.,Â those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these procedures and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the blanket tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems in the determination of the limiting distribution of the test statistics under composite null hypotheses, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.

Omnibus Goodness-of-Fit Tests for Copulas: A Review and a Power Study

A review of fuzzy set aggregation connectives

A class of ra-variate distributions with given margins and m(m ? l)/2 dependence parameters, which is based on iteratively mixing conditional distributions, is derived. The family of multivariate normal distributions is a special case. The motivation for the class is to get parametric families that have m(m ? l)/2 dependence parameters and properties that the family of multivariate normal distributions does not have. Properties of the class are studied, with details for (i) conditions for bivariate tail dependence and non-trivial limiting multivariate extreme value distributions and (ii) range of dependence for a bivariate measure of association such as Kendall's tau.

M.J. Frank

Papers

On the simultaneous associativity of F(x, y) and x+y-F(x, y). (Short Communication).