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51
PairCopula Constructions of Multiple Dependence
"... Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution an ..."
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Cited by 42 (12 self)
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Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution and propose a method to perform inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using paircopulae as simple building blocs. Paircopula decomposed models also represent a very exible way to construct higherdimensional coplulae. We apply the methodology to a nancial data set. Our approach represents the rst step towards developing of an unsupervised algorithm that explores the space of possible paircopula models, that also can be applied to huge data sets automatically.
Copula goodnessoffit testing: an overview and power comparison
, 2007
"... Abstract. Several copula goodnessoffit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different app ..."
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Cited by 18 (1 self)
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Abstract. Several copula goodnessoffit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different approaches. While no approach is always the best, some stand out and conclusions and recommendations are made. A novel study of pvalue variation due to permuation order, for approaches based on Rosenblatt’s transformation is also carried out. Results show significant variation due to permutation order for some of the approaches based on this transform. However, when approaching rejection regions, the additional variation is negligible.
Models and Measures for Correlation in CyberInsurance
 IN FIFTH WORKSHOP ON THE ECONOMICS OF INFORMATION SECURITY
, 2006
"... High correlation in failure of information systems due to worms and viruses has been cited as major impediment to cyberinsurance. However, of the many cyberrisk classes that influence failure of information systems, not all exhibit similar correlation properties. In this paper, we introduce a n ..."
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Cited by 17 (4 self)
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High correlation in failure of information systems due to worms and viruses has been cited as major impediment to cyberinsurance. However, of the many cyberrisk classes that influence failure of information systems, not all exhibit similar correlation properties. In this paper, we introduce a new classification of correlation properties of cyberrisks based on a twintier approach. At the first tier, is the correlation of cyberrisks within a firm i.e. correlated failure of multiple systems on its internal network. At second tier, is the correlation in risk at a global level i.e. correlation across independent firms in an insurer's portfolio. Various classes of cyberrisks exhibit di#erent level of correlation at two tiers, for instance, insider attacks exhibit high internal but low global correlation. While internal risk correlation within a firm influences its decision to seek insurance, the global correlation influences insurers' decision in setting the premium. Citing real data we study the combined dynamics of the twostep risk arrival process to determine conditions conducive to the existence of cyberinsurance market. We address
FAST SIMULATION FOR MULTIFACTOR PORTFOLIO CREDIT RISK IN THE tCOPULA MODEL
, 2005
"... We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the tcopula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and ..."
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Cited by 16 (2 self)
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We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the tcopula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and a scaled chisquare random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chisquare random variable. Then, conditional on the chisquare random variable, we apply the importance sampling procedure developed for the Gaussian copula model in Glasserman, Kang, Shahabuddin (2005b). We support our importance sampling procedure by numerical examples.
A TwoFactor Error Model for Quantitative Steganalysis
"... Quantitative steganalysis refers to the exercise not only of detecting the presence of hidden stego messages in carrier objects, but also of estimating the secret message length. This problem is well studied, with many detectors proposed but only a sparse analysis of errors in the estimators. A deep ..."
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Cited by 13 (10 self)
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Quantitative steganalysis refers to the exercise not only of detecting the presence of hidden stego messages in carrier objects, but also of estimating the secret message length. This problem is well studied, with many detectors proposed but only a sparse analysis of errors in the estimators. A deep understanding of the error model, however, is a fundamental requirement for the assessment and comparison of different detection methods. This paper presents a rationale for a twofactor model for sources of error in quantitative steganalysis, and shows evidence from a dedicated largescale nested experimental setup with a total of more than 200 million attacks. Apart from general findings about the distribution functions found in both classes of errors, their respective weight is determined, and implications for statistical hypothesis tests in benchmarking scenarios or regression analyses are demonstrated. The results are based on a rigorous comparison of five different detection methods under many different external conditions, such as size of the carrier, previous JPEG compression, and colour channel selection. We include analyses demonstrating the effects of local variance and cover saturation on the different sources of error, as well as presenting the case for a relative bias model for betweenimage error.
Asymptotic results for the sum of dependent nonidentically distributed random variables, Methodology and Computing
 in Applied Probability. Forthcoming. DOI
, 2008
"... In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of nonidentically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria ..."
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Cited by 9 (0 self)
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In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of nonidentically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which, even for regularly varying marginal distributions, no asymptotic limit of the tail sum exists. Some explicit calculations for diagonal copulas and tcopulas are given. 1
Modelling Longitudinal Data using a PairCopula Decomposition of Serial Dependence
, 2009
"... Copulas have proven to be very successful tools for the flexible modelling of crosssectional dependence. In this paper we express the dependence structure of continuous time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a ‘vine ’ in t ..."
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Cited by 6 (3 self)
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Copulas have proven to be very successful tools for the flexible modelling of crosssectional dependence. In this paper we express the dependence structure of continuous time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a ‘vine ’ in the graphical models literature, where each copula is entitled a ‘paircopula’. We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence paircopulas, with the end result being a parsimonious representation of a timeinhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Overall, the paircopula construction is very general and the Bayesian approach generalises many previous methods for the analysis of longitudinal data. Both the reliability of the proposed Bayesian methodology, and the advantages of the paircopula formulation, are demonstrated via simulation and two examples. The first is an agricultural science example, while the second is an econometric model for the forecasting of intraday electricity load. For both examples the Bayesian paircopula model is substantially more flexible than longitudinal models employed previously.
Nonparametric inference for bivariate extremevalue copulas
 In Extreme Value Distributions (Editors: M. Ahsanullah, S. Kirmani) Nova Science Publishers
, 2007
"... Consider a continuous random pair (X, Y) whose dependence is characterized by an extremevalue copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickan ..."
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Cited by 6 (1 self)
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Consider a continuous random pair (X, Y) whose dependence is characterized by an extremevalue copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859–878] and Capéraà, Fougères and Genest [Biometrika 84 (1997) 567–577]. In this paper, rankbased versions of these estimators are proposed for the more common case where the margins of X and Y are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rankbased estimators. Their finite and largesample performance is then compared to that of their knownmargin analogues, as well as with endpointcorrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also suggested. 1. Introduction. Let (X,Y
PairCopula Constructions of Multiple Dependence
"... Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution an ..."
Abstract

Cited by 4 (3 self)
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Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution and propose a method to perform inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using paircopulae as simple building blocs. Paircopula decomposed models also represent a very exible way to construct higherdimensional coplulae. We apply the methodology to a nancial data set. Our approach represents the rst step towards developing of an unsupervised algorithm that explores the space of possible paircopula models, that also can be applied to huge data sets automatically.
TESTING FOR STRUCTURAL CHANGES IN EXCHANGE RATES DEPENDENCE BEYOND LINEAR CORRELATION
, 2007
"... In this paper we test for structural changes in the conditional dependence of twodimensional foreign exchange data. We show that by modeling the conditional dependence structure using copulae we can detect changes in the dependence beyond linear correlation like changes in the tail of the joint dist ..."
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Cited by 4 (0 self)
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In this paper we test for structural changes in the conditional dependence of twodimensional foreign exchange data. We show that by modeling the conditional dependence structure using copulae we can detect changes in the dependence beyond linear correlation like changes in the tail of the joint distribution. This methodology is relevant for estimating risk management measures as portfolio ValueatRisk, pricing multiname financial instruments and portfolio asset allocation. Our results include evidence of the existence of changes in the correlation as well as in the fatness of the tail of the dependence between Deutsche Mark and Japanese Yen.