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Title:

Bayesian Inference for Multivariate Copulas Using Pair-Copula Constructions

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We provide a Bayesian analysis of pair-copula constructions (PCCs) (Aas et al., 2009), which outperform many other multivariate copula constructions in modeling dependencies in financial data. We use bivariate t-copulas as building blocks in a PCC to allow extreme events in bivariate margins individually. While parameters may be estimated by max...

We provide a Bayesian analysis of pair-copula constructions (PCCs) (Aas et al., 2009), which outperform many other multivariate copula constructions in modeling dependencies in financial data. We use bivariate t-copulas as building blocks in a PCC to allow extreme events in bivariate margins individually. While parameters may be estimated by maximum likelihood, confidence intervals are difficult to obtain. Consequently, we develop a Markov chain Monte Carlo (MCMC) algorithm and compute credible intervals. Standard errors obtained from MCMC output are compared to those obtained from a numerical Hessian matrix and bootstrapping. As applications, we consider Norwegian financial returns and Euro swap rates. Finally, we apply the Bayesian model selection approach of Congdon (2006) to identify conditional independence, thus constructing more parsimonious PCCs. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press. Minimize

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Pair-copula constructions for modeling exchange rate dependence

Pair-copula constructions for modeling exchange rate dependence Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-11-19

Source:

http://www-m4.ma.tum.de/Papers/Czado/czado-min-baumann-dakovic.pdf

http://www-m4.ma.tum.de/Papers/Czado/czado-min-baumann-dakovic.pdf Minimize

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text

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en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Bayesian inference for multivariate copulas using pair-copula

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constructions

constructions Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-11-19

Source:

http://www-m4.ma.tum.de/Papers/Min/Min-Czado-Bayesian-Infrence.pdf

Document Type:

text

Language:

en

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JEL classification ; C11 ; C51 ; C52

JEL classification ; C11 ; C51 ; C52 Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Testing for zero-modification in count regression models

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Count data often exhibit overdispersion and/or require an adjustment for zero outcomes with respect to a Poisson model. Zero-modified Poisson (ZMP) and zeromodified generalized Poisson (ZMGP) regression models are useful classes of models for such data. In the literature so far only score tests are used for testing the necessity of this adjustme...

Count data often exhibit overdispersion and/or require an adjustment for zero outcomes with respect to a Poisson model. Zero-modified Poisson (ZMP) and zeromodified generalized Poisson (ZMGP) regression models are useful classes of models for such data. In the literature so far only score tests are used for testing the necessity of this adjustment. We address this problem by using Wald and likelihood ratio tests. We show how poor the performance of the score tests can be in comparison to the performance of Wald and likelihood ratio (LR) tests through a simulation study. In particular, the score test in the ZMP case results in a power loss of 47 % compared to the Wald test in the worst case, while in the ZMGP case the worst loss is 87%. Therefore, regardless of the computational advantage of score tests, the loss in power compared to the Wald and LR tests should not be neglected and these much more powerful alternatives should be used instead. We prove consistency and asymptotic normality of the maximum likelihood estimates in ZGMP regression models, on what Wald and likelihood ratio tests rely. The usefulnes of ZGMP models is illustrated in a real data example. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-03-22

Source:

http://www-m4.ma.tum.de/Papers/Czado/Min-Czado-Testing-for-zero-modification.pdf

http://www-m4.ma.tum.de/Papers/Czado/Min-Czado-Testing-for-zero-modification.pdf Minimize

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text

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en

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generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimate ; overdispersion ; score test ; Wald test ; zero-inflation ; zero-modification Running title ; Testing for zero-modificationTESTING FOR ZERO-MODIFICATION 2

generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimate ; overdispersion ; score test ; Wald test ; zero-inflation ; zero-modification Running title ; Testing for zero-modificationTESTING FOR ZERO-MODIFICATION 2 Minimize

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310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Bayesian model selection for D-vine pair-copula constructions

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Inrecent years analysesofdependence structuresusing copulashave becomemorepopular than the standard correlation analysis. Starting from Aas, Czado, Frigessi, and Bakken (2009) regular vine pair-copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence pres...

Inrecent years analysesofdependence structuresusing copulashave becomemorepopular than the standard correlation analysis. Starting from Aas, Czado, Frigessi, and Bakken (2009) regular vine pair-copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence present indatacansimplifyandreducethemsignificantly. Inthispapertheauthorsdetect (conditional) independence in a particular vine PCC model based on bivariate t−copulas by deriving and implementing a reversible jump Markov chain Monte Carlo algorithm. However the methodology is general and can be extended to any regular vine PCC and to all known bivariate copula families. The proposed approach considers model selection andestimationproblemsforPCCssimultaneously. Theeffectiveness ofthedeveloped algorithm isshown insimulations andits usefulness is illustrated in two real dataapplications. Keywords: copula, D-vine, Metropolis-Hastings algorithm, pair-copula construction, reversible jump Markov chain Monte Carlo. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-24

Source:

http://www-m4.ma.tum.de/Papers/Czado/Min-Czado-RJMCMC.pdf

http://www-m4.ma.tum.de/Papers/Czado/Min-Czado-RJMCMC.pdf Minimize

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text

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en

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Title:

Testing for zero-modification in count regression

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models

models Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.ma.tum.de/Papers/Czado/Czado-Min.pdf

http://www-m4.ma.tum.de/Papers/Czado/Czado-Min.pdf Minimize

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text

Language:

en

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generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimator ; overdispersion ; score test ; Wald test ; zero-modification 1 Corresponding author. Fax ; 49/89/289-17435

generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimator ; overdispersion ; score test ; Wald test ; zero-modification 1 Corresponding author. Fax ; 49/89/289-17435 Minimize

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Title:

Testing for zero-modification in count regression

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models

models Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.ma.tum.de/Papers/Czado/Czado-Min.ps

http://www-m4.ma.tum.de/Papers/Czado/Czado-Min.ps Minimize

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text

Language:

en

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generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimator ; overdispersion ; score test ; Wald test ; zero-modification 1 Corresponding author. Fax ; 49/89/289-17435

generalized Poisson distribution ; likelihood ratio test ; maximum likelihood estimator ; overdispersion ; score test ; Wald test ; zero-modification 1 Corresponding author. Fax ; 49/89/289-17435 Minimize

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Title:

Zero-inflated generalized Poisson regression models: Asymptotic theory and applications

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MSC 2000: Primary 62J02; secondary 62F12. Abstract: Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zero-inflation occur. In this paper we study regression models associated with the generalized Poisson distribution (Consul (1989)). These regression models which ...

MSC 2000: Primary 62J02; secondary 62F12. Abstract: Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zero-inflation occur. In this paper we study regression models associated with the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by McCullagh and Nelder (1989) for which an established asymptotic theory is available. We prove consistency and asymptotic normality of the maximum likelihood estimators in zero-inflated generalized Poisson regression models. Further the accuracy of the asymptotic normality approximation is investigated through a simulation study. It is also shown that a Wald test for detecting zero-inflation or zero-deflation based on our results is considerable more powerful than the score test in zero-modified Poisson regression models. The usefulness of the considered models is demonstrated in two applications. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Min/Czado-Min.pdf

Document Type:

text

Language:

en

Subjects:

estimator ; overdispersion ; Wald test ; zero-deflation ; zero-inflation

estimator ; overdispersion ; Wald test ; zero-deflation ; zero-inflation Minimize

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310 Collections of general statistics *(computed)*

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Title:

Analysis of Australian electricity loads using joint Bayesian inference of D-Vines with autoregressive margins

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Sklar’s theorem allows the construction of models for dependent components using a multivariate copula together with marginal distributions. For estimation of the copula and marginal parameters, a two step procedure is often used to avoid high dimensional optimization. Here, marginal parameters are estimated first, then used to transform to unif...

Sklar’s theorem allows the construction of models for dependent components using a multivariate copula together with marginal distributions. For estimation of the copula and marginal parameters, a two step procedure is often used to avoid high dimensional optimization. Here, marginal parameters are estimated first, then used to transform to uniform margins and in a second step, the copula parameters are estimated. This procedure is not efficient. Therefore, we follow a joint estimation approach in a Bayesian framework using Markov Chain Monte Carlo (MCMC) methods. This allows also for the assessment of parameter uncertainty using credible intervals. D-Vine copulas are utilized and as marginal models we allow for autoregressive models of first order. Finally, we apply these methods to Australian electricity loads demonstrating the usefulness of this approach. Bayesian model selection is also discussed and applied using a method suggested by Congdon (2006). Keywords: multivariate copulas, vines, AR(1) margins, Bayesian inference, MCMC 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-11-19

Source:

http://www-m4.ma.tum.de/Papers/Czado/Czado-Gaertner-Min.pdf

http://www-m4.ma.tum.de/Papers/Czado/Czado-Gaertner-Min.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Title:

Almost sure limit theorems for U-statistics

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We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki (2001). We extend this result to the case of convergence to stable laws and also prove a functional version. MSC: 60F05, 60F17

We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki (2001). We extend this result to the case of convergence to stable laws and also prove a functional version. MSC: 60F05, 60F17 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Min/Holzmann-Koch-Min.pdf

Document Type:

text

Language:

en

Subjects:

Almost sure limit theorem ; Functional limit theorem ; Stable distributions ; U-statistics 1

Almost sure limit theorem ; Functional limit theorem ; Stable distributions ; U-statistics 1 Minimize

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