CDVine-Package

Package‘CDVine’August29,2013TypePackageTitleStatisticalinferenceofC-andD-vinecopulasVersion1.1-13Date2013-08-12AuthorUlfSchepsmeier,[e-mail](=2.11.0),MASS,mvtnorm,igraphDescriptionThispackageprovidesfunctionsforstatisticalinferenceofcanonicalvine(C-vine)andD-vinecopulas.Itcontainstoolsforbivariateexploratorydataanalysisandforbivariateaswellasvinecopulaselection.Modelscanbeestimatedeithersequentiallyorbyjointmaximumlikelihoodestimation.Samplingalgorithmsandplottingmethodsarealsoincluded.Dataisassumedtolieintheunithypercube(so-calledcopuladata).LicenseGPL(=2)LazyLoadyesNeedsCompilationyesRepositoryCRANDate/Publication2013-08-2615:43:50Rtopicsdocumented:CDVine-package......................................2BiCopCDF.........................................5BiCopChiPlot........................................6BiCopEst..........................................8BiCopGofKendall......................................1112CDVine-packageBiCopHfunc.........................................13BiCopIndTest........................................16BiCopKPlot.........................................17BiCopLambda........................................19BiCopMetaContour.....................................22BiCopName.........................................25BiCopPar2TailDep.....................................26BiCopPar2Tau........................................29BiCopPDF..........................................31BiCopSelect.........................................33BiCopSim..........................................36BiCopTau2Par........................................37BiCopVuongClarke.....................................39CDVineAIC-BIC......................................41CDVineClarkeTest.....................................44CDVineCopSelect......................................47CDVineLogLik.......................................49CDVineMLE........................................52CDVinePar2Tau.......................................55CDVineSeqEst.......................................56CDVineSim.........................................59CDVineTreePlot.......................................61CDVineVuongTest.....................................64worldindices.........................................67Index68CDVine-packageStatisticalinferenceofC-andD-vinecopulasDescriptionThispackageprovidesfunctionsforstatisticalinferenceofcanonicalvine(C-vine)andD-vinecopulas.Itcontainstoolsforbivariateexploratorydataanalysisandforbivariateaswellasvinecopulaselection.Modelscanbeestimatedeithersequentiallyorbyjointmaximumlikelihoodestimation.Samplingalgorithmsandplottingmethodsarealsoincluded.Dataisassumedtolieintheunithypercube(so-calledcopuladata).DetailsPackage:CDVineType:PackageVersion:1.1-13Date:2013-08-12License:GPL(=2)Depends:R(2:11:0),MASS,mvtnorm,igraphLazyLoad:yesCDVine-package3BivariatecopulafamiliesInthispackageseveralbivariatecopulafamiliesareincludedforbivariateanalysisaswellasformultivariateanalysisusingvinecopulas.Itprovidesfunctionalityofelliptical(GaussianandStu-dentt)aswellasArchimedean(Clayton,Gumbel,Frank,Joe,BB1,BB6,BB7andBB8)copulastocoveralargebandwidthofpossibledependencestructures.FortheArchimedeancopulafamiliesrotatedversionsareincludedtocovernegativedependencetoo.ThetwoparameterBB1,BB6,BB7andBB8copulasarehowevernumericallyinstableforlargeparameters,inparticular,ifBB6,BB7andBB8copulasareclosetotheJoecopulawhichisaboundarycaseofthesethreecopulafamilies.Ingeneral,theusershouldbecarefulwithextremeparameterchoices.Thefollowingtableshowstheparameterrangesofbivariatecopulafamilieswithparametersparandpar2:Copulafamilyparpar2Gaussian(1;1)-Studentt(1;1)(2;1)(Survival)Clayton(0;1)-(Survival)Gumbel[1;1)-FrankRnf0g-(Survival)Joe(1;1)-RotatedClayton(90and270degrees)(1;0)-RotatedGumbel(90and270degrees)(1;1]-RotatedJoe(90and270degrees)(1;1)-(Survival)Clayton-Gumbel(BB1)(0;1)[1;1)(Survival)Joe-Gumbel(BB6)[1;1)[1;1)(Survival)Joe-Clayton(BB7)[1;1)(0;1)(Survival)Joe-Frank(BB8)[1;1)(0;1]RotatedClayton-Gumbel(90and270degrees)(1;0)1;1]RotatedJoe-Gumbel(90and270degrees)(1;1](1;1]RotatedJoe-Clayton(90and270degrees)(1;1](1;0)RotatedJoe-Frank(90and270degrees)(1;1][1;0)C-andD-vinecopulamodelsWhenspecifyingC-andD-vinecopulamodels,onehastoselectanorderofthevariables.ForaD-vinetheorderofthevariablesinthefirsttreehastobechosenandforaC-vinetherootnodesforeachtreeneedtobedetermined.FunctionsforinferenceofC-andD-vinecopulamodelsinthispackageassumethattheorderofthevariablesinthedatasetunderinvestigationexactlycor-respondstothisC-orD-vineorder.E.g.,inaC-vinethefirstcolumnofadatasetisthefirstrootnode,thesecondcolumnthesecondrootnode,etc.AccordingtothisorderargumentshavetobeprovidedtofunctionsforC-andD-vinecopulainference.Afterchoosingthetypeofthevinemodel,thecopulafamilies(family)andparameters(parandpar2)havetobespecifiedasvectorsoflengthd(d1)=2,wheredisthenumberofvariables.InaC-vine,theentriesofthisvectorcorrespondtothefollowingpairsandassociatedpair-copulaterm