We propose a parametric version of Independent Component Analysis (ICA) via Copulas families of multivariate distributions that join univariate margins to multivariate distributions. Our procedure exploits the role for copula models in information theory and in measures of association, specifically: the use of copulae densities as parametric mutual information, and as measures of association on...

Multivariate hydrologic frequency analysis has been widely studied using: (1) commonly known joint distributions or copula functions with the assumption of univariate variables being independently identically distributed (I.I.D.) random variables; or (2) directly applying the entropy theory-based framework. However, for the I.I.D. univariate random variable assumption, the univariate variable m...

The cumulative distribution network (CDN) [21] is a recently developed class of probabilistic graphical models (PGMs) permitting a copula factorization, in which the CDF, rather than the density, is factored. Despite there being much recent interest within the machine learning community about copula representations, there has been scarce research into the CDN, its amalgamation with copula theor...

Empirical studies show that there is stronger dependency between large losses than large profit in financial market, which undermine the performance of using symmetric distribution for modeling these asymmetric. That is why the assuming normal joint distribution of returns is not suitable because of considering the linier dependence, and can be lead to inappropriate estimate of VaR. Copula theo...

Copula is a function which can link two or more marginal distributions together to form a joint distribution. This paper aims to analyze the dependence between Shanghai and Shenzhen stock markets using copula theory based on GARCH. We use the synchronous 100 times daily returns data and copula based GARCH to model the joint distribution of stock index returns because copula based GARCH can fit ...

In this paper, we briefly review the basics of copula theory and the problem of estimating Value at Risk (VaR) of portfolio composed by several assets. We present two VaR estimation models in which each return series is assumed to follow AR(1)-GARCH(1, 1) model and the innovations are simultaneously generated using Gaussian copula and Student t copula. The presented models are applied to estima...

The entropy theory has been widely applied in hydrology for probability inference based on incomplete information and the principle of maximum entropy. Meanwhile, copulas have been extensively used for multivariate analysis and modeling the dependence structure between hydrologic and climatic variables. The underlying assumption of the principle of maximum entropy is that the entropy variables ...

This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions h...

In this paper we present a novel Bayesian approach for default probability estimation. The methodology is based on multivariate contingent claim analysis and pair copula theory. Balance sheet data are used to asses the firm value and to compute its default probability. The firm pricing function is obtained via a pair copula approach, and Monte Carlo simulations are used to calculate the default...