1,393 research outputs found
Extension of dependence properties to semi-copulas and applications to the mean–variance model
This paper deals with the construction of a semi-copula D, not necessarily exchangeable, whose “dependence” properties translate remarkable aspects of investors’ behavior. To achieve this aim, we propose a new version of the standard mean-variance framework. For our purpose, a particular class of utility functions G has been introduced. The induced
transformation of G is considered and the definition of semi-copula D hinges on the family of the indifference curves of G
Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property
We first review an approach that had been developed in the past years to
introduce concepts of "bivariate ageing" for exchangeable lifetimes and to
analyze mutual relations among stochastic dependence, univariate ageing, and
bivariate ageing. A specific feature of such an approach dwells on the concept
of semi-copula and in the extension, from copulas to semi-copulas, of
properties of stochastic dependence. In this perspective, we aim to discuss
some intricate aspects of conceptual character and to provide the readers with
pertinent remarks from a Bayesian Statistics standpoint. In particular we will
discuss the role of extensions of dependence properties. "Archimedean" models
have an important role in the present framework. In the second part of the
paper, the definitions of Kendall distribution and of Kendall equivalence
classes will be extended to semi-copulas and related properties will be
analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean"
models and extend to them the analysis of the relations between the ageing
notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD
Extreme-Value Copulas
Being the limits of copulas of componentwise maxima in independent random
samples, extreme-value copulas can be considered to provide appropriate models
for the dependence structure between rare events. Extreme-value copulas not
only arise naturally in the domain of extreme-value theory, they can also be a
convenient choice to model general positive dependence structures. The aim of
this survey is to present the reader with the state-of-the-art in dependence
modeling via extreme-value copulas. Both probabilistic and statistical issues
are reviewed, in a nonparametric as well as a parametric context.Comment: 20 pages, 3 figures. Minor revision, typos corrected. To appear in F.
Durante, W. Haerdle, P. Jaworski, and T. Rychlik (editors) "Workshop on
Copula Theory and its Applications", Lecture Notes in Statistics --
Proceedings, Springer 201
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
Robustness of a semiparametric estimator of a copula
Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable. A semiparametric method for estimating the dependence parameters of copulas was proposed by Genest, Ghoudi and Rivest (1995), in which the marginal distributions are estimated nonparameterically by empirical distribution functions. Thus, this method does not require any marginal distribution to have a known parametric form. However, a standard concern about semiparametric methods is the possibility that it may be substantially less efficient than the parametric method when the model is completely parametric and correctly specified. In this paper we investigate the efficiency-robustness properties of the foregoing semiparametric method by simulation; in particular, we evaluate the performance of this method when the marginal distributions are specified correctly and when they are specified incorrectly. The results show that the semiparametric method is better than the parametric methods. An example involving the household expenditure data for Australia is used to compare and contrast the methodsCopulas; multivariate joint distribution; inference function method;maximum likelihood mathod;semiparametric method
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