3,167 research outputs found
Invariant copulas
summary:Copulas which are invariant with respect to the construction of the corresponding survival copula and other related dualities are studied. A full characterization of invariant associative copulas is given
Efficient Estimation of Copula-based Semiparametric Markov Models
This paper considers efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions; where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that Markov processes generated via Clayton, Gumbel and Student's copulas and their survival copulas are all geometrically ergodic. We then propose a sieve maximum likelihood estimation (MLE) for the copula parameter, the invariant distribution and the conditional quantiles. We show that the sieve MLEs of any smooth functionals are root- consistent, asymptotically normal and efficient; and that their sieve likelihood ratio statistics are asymptotically chi-square distributed. We present Monte Carlo studies to compare the finite sample performance of the sieve MLE, the two-step estimator of Chen and Fan (2006), the correctly specified parametric MLE and the incorrectly specified parametric MLE. The simulation results indicate that our sieve MLEs perform very well; having much smaller biases and smaller variances than the two-step estimator for Markov models generated via Clayton, Gumbel and other tail dependent copulas.Copula, Tail dependence, Nonlinear Markov models, Geometric ergodicity, Sieve MLE, Semiparametric efficiency, Sieve likelihood ratio statistics, Value-at-Risk
An information theoretic approach to statistical dependence: copula information
We discuss the connection between information and copula theories by showing
that a copula can be employed to decompose the information content of a
multivariate distribution into marginal and dependence components, with the
latter quantified by the mutual information. We define the information excess
as a measure of deviation from a maximum entropy distribution. The idea of
marginal invariant dependence measures is also discussed and used to show that
empirical linear correlation underestimates the amplitude of the actual
correlation in the case of non-Gaussian marginals. The mutual information is
shown to provide an upper bound for the asymptotic empirical log-likelihood of
a copula. An analytical expression for the information excess of T-copulas is
provided, allowing for simple model identification within this family. We
illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter
Evolution of the Dependence of Residual Lifetimes
We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
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