1,531 research outputs found
Final solution to the problem of relating a true copula to an imprecise copula
In this paper we solve in the negative the problem proposed in this journal
(I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and
Systems, 278 (2015), 48-66) whether an order interval defined by an imprecise
copula contains a copula. Namely, if is a nonempty set of
copulas, then and are quasi-copulas and the pair
is an imprecise copula according to the
definition introduced in the cited paper, following the ideas of -boxes. We
show that there is an imprecise copula in this sense such that there is
no copula whatsoever satisfying . So, it is
questionable whether the proposed definition of the imprecise copula is in
accordance with the intentions of the initiators. Our methods may be of
independent interest: We upgrade the ideas of Dibala et al. (Defects and
transformations of quasi-copulas, Kybernetika, 52 (2016), 848-865) where
possibly negative volumes of quasi-copulas as defects from being copulas were
studied.Comment: 20 pages; added Conclusion, added some clarifications in proofs,
added some explanations at the beginning of each section, corrected typos,
results remain the sam
Quasi-random numbers for copula models
The present work addresses the question how sampling algorithms for commonly
applied copula models can be adapted to account for quasi-random numbers.
Besides sampling methods such as the conditional distribution method (based on
a one-to-one transformation), it is also shown that typically faster sampling
methods (based on stochastic representations) can be used to improve upon
classical Monte Carlo methods when pseudo-random number generators are replaced
by quasi-random number generators. This opens the door to quasi-random numbers
for models well beyond independent margins or the multivariate normal
distribution. Detailed examples (in the context of finance and insurance),
illustrations and simulations are given and software has been developed and
provided in the R packages copula and qrng
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
Improved Frechet bounds and model-free pricing of multi-asset options
Improved bounds on the copula of a bivariate random vector are computed when
partial information is available, such as the values of the copula on a given
subset of , or the value of a functional of the copula, monotone with
respect to the concordance order. These results are then used to compute
model-free bounds on the prices of two-asset options which make use of extra
information about the dependence structure, such as the price of another
two-asset option.Comment: Replaced with revised versio
Asymptotically distribution-free goodness-of-fit testing for tail copulas
Let be an i.i.d. sample from a bivariate
distribution function that lies in the max-domain of attraction of an extreme
value distribution. The asymptotic joint distribution of the standardized
component-wise maxima and is then
characterized by the marginal extreme value indices and the tail copula . We
propose a procedure for constructing asymptotically distribution-free
goodness-of-fit tests for the tail copula . The procedure is based on a
transformation of a suitable empirical process derived from a semi-parametric
estimator of . The transformed empirical process converges weakly to a
standard Wiener process, paving the way for a multitude of asymptotically
distribution-free goodness-of-fit tests. We also extend our results to the
-variate () case. In a simulation study we show that the limit theorems
provide good approximations for finite samples and that tests based on the
transformed empirical process have high power.Comment: Published at http://dx.doi.org/10.1214/14-AOS1304 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Out-of-sample comparison of copula specifications in multivariate density forecasts
We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or nonnested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student’s t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.Copula-based density forecast; semiparametric statistics; out-of-sample forecast evaluation; Kullback-Leibler Information Criterion; empirical copula
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