R: Multivariate Dependence Modeling with Copulas

copula-package {copula} | R Documentation

## Multivariate Dependence Modeling with Copulas

### Description

The copula package provides (S4) classes of commonly used elliptical, (nested) Archimedean, extreme value and other copula families; methods for density, distribution, random number generation, and plots.

Fitting copula models and goodness-of-fit tests. Independence and serial (univariate and multivariate) independence tests, and other copula related tests.

### Details

The DESCRIPTION file:

Package: | copula
Version: | 1.0-1
VersionNote: | Last CRAN: 1.0-0 on 2020-05-19
Date: | 2020-12-07
Title: | Multivariate Dependence with Copulas
Authors@R: | c(person("Marius", "Hofert", role = "aut", email = "marius.hofert@uwaterloo.ca", comment = c(ORCID = "0000-0001-8009-4665")) , person("Ivan", "Kojadinovic", role = "aut", email = "ivan.kojadinovic@univ-pau.fr", comment = c(ORCID = "0000-0002-2903-1543")) , person("Martin","Maechler", role=c("aut","cre"), email="maechler@stat.math.ethz.ch", comment = c(ORCID = "0000-0002-8685-9910")) , person("Jun", "Yan", rol = "aut", email = "jun.yan@uconn.edu", comment = c(ORCID = "0000-0003-4401-7296")) , person(c("Johanna", "G."), "Nešlehová", role = "ctb", comment = c("evTestK()", ORCID = "0000-0001-9634-4796")) , person("Rebecca", "Morger", role = "ctb", comment = "fitCopula.ml(): code for free mixCopula weight parameters") )
Depends: | R (>= 3.5.0)
Imports: | stats, graphics, methods, stats4, Matrix, lattice, colorspace, gsl, ADGofTest, stabledist (>= 0.6-4), mvtnorm, pcaPP, pspline, numDeriv
Suggests: | MASS, KernSmooth, sfsmisc, scatterplot3d, Rmpfr, bbmle, knitr, rmarkdown, abind, crop, gridExtra, lcopula, mev, mvnormtest, parallel, partitions, polynom, qrng, randtoolbox, rugarch, Runuran, tseries, VGAM, VineCopula, zoo
SuggestsNote: | packages abind, ..., zoo (last lines above) are only used in vignettes, demos and a few tests.
VignetteBuilder: | knitr
Enhances: | nor1mix, copulaData
SystemRequirements: | pdfcrop (part of TexLive) is required to rebuild the vignettes.
Description: | Classes (S4) of commonly used elliptical, Archimedean, extreme-value and other copula families, as well as their rotations, mixtures and asymmetrizations. Nested Archimedean copulas, related tools and special functions. Methods for density, distribution, random number generation, bivariate dependence measures, Rosenblatt transform, Kendall distribution function, perspective and contour plots. Fitting of copula models with potentially partly fixed parameters, including standard errors. Serial independence tests, copula specification tests (independence, exchangeability, radial symmetry, extreme-value dependence, goodness-of-fit) and model selection based on cross-validation. Empirical copula, smoothed versions, and non-parametric estimators of the Pickands dependence function.
License: | GPL (>= 3) | file LICENCE
ByteCompile: | yes
Collate: | AllClass.R Classes.R AllGeneric.R Auxiliaries.R aux-acopula.R asymCopula.R mixCopula.R rotCopula.R Copula.R special-func.R amhCopula.R claytonCopula.R frankCopula.R cop_objects.R nacopula.R dC-dc.R amhExpr.R An.R archmCopula.R cCopula.R claytonExpr.R ellipCopula.R empCopula.R empPsi.R acR.R estimation.R evCopula.R evTests.R exchTests.R fgmCopula.R fitCopula.R fitLambda.R fitMvdc.R fixedPar.R frankExpr.R galambosCopula.R galambosExpr-math.R galambosExpr.R ggraph-tools.R pairsRosenblatt.R prob.R gofTrafos.R gofEVTests.R gofCopula.R graphics.R gumbelCopula.R gumbelExpr.R huslerReissCopula.R huslerReissExpr.R indepCopula.R fhCopula.R lowfhCopula.R upfhCopula.R indepTests.R joeCopula.R K.R logseries.R mvdc.R margCopula.R matrix_tools.R normalCopula.R opower.R plackettCopula.R plackettExpr.R moCopula.R rstable1.R safeUroot.R schlatherCopula.R stable.R timing.R tCopula.R tawnCopula.R tawnExpr.R tevCopula.R varianceReduction.R wrapper.R xvCopula.R zzz.R
Encoding: | UTF-8
URL: | http://copula.r-forge.r-project.org/
Author: | Marius Hofert [aut] (<https://orcid.org/0000-0001-8009-4665>), Ivan Kojadinovic [aut] (<https://orcid.org/0000-0002-2903-1543>), Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Jun Yan [aut] (<https://orcid.org/0000-0003-4401-7296>), Johanna G. Nešlehová [ctb] (evTestK(), <https://orcid.org/0000-0001-9634-4796>), Rebecca Morger [ctb] (fitCopula.ml(): code for free mixCopula weight parameters)
Maintainer: | Martin Maechler <maechler@stat.math.ethz.ch>
Repository: | R-Forge
Repository/R-Forge/Project: | copula
Repository/R-Forge/Revision: | 1850
Repository/R-Forge/DateTimeStamp: | 2020-12-11 15:17:41
Date/Publication: | 2020-12-11 15:17:41

Index of help topics:

    .pairsCond              Pairs Plot of a cu.u Object (Internal Use)
    A..Z                    Sinc, Zolotarev's, and Other Mathematical
                            Utility Functions
    An                      Nonparametric Rank-based Estimators of the
                            Pickands Dependence Function
    Bernoulli               Compute Bernoulli Numbers
    Copula                  Density, Evaluation, and Random Number
                            Generation for Copula Functions
    Eulerian                Eulerian and Stirling Numbers of First and
                            Second Kind
    K                       Kendall Distribution Function for Archimedean
                            Copulas
    Mvdc                    Multivariate Distributions Constructed from
                            Copulas
    RSpobs                  Pseudo-Observations of Radial and Uniform Part
                            of Elliptical and Archimedean Copulas
    SMI.12                  SMI Data - 141 Days in Winter 2011/2012
    Sibuya                  Sibuya Distribution - Sampling and
                            Probabilities
    absdPsiMC               Absolute Value of Generator Derivatives via
                            Monte Carlo
    acopula-class           Class "acopula" of Archimedean Copula Families
    acopula-families        Specific Archimedean Copula Families ("acopula"
                            Objects)
    allComp                 All Components of a (Inner or Outer) Nested
                            Archimedean Copula
    archmCopula             Construction of Archimedean Copula Class Object
    archmCopula-class       Class "archmCopula"
    beta.                   Sample and Population Version of Blomqvist's
                            Beta for Archimedean Copulas
    cCopula                 Conditional Distributions and Their Inverses
                            from Copulas
    cloud2-methods          Cloud Plot Methods ('cloud2') in Package
                            'copula'
    coeffG                  Coefficients of Polynomial used for Gumbel
                            Copula
    contour-methods         Methods for Contour Plots in Package 'copula'
    contourplot2-methods    Contour Plot Methods 'contourplot2' in Package
                            'copula'
    copula-class            Mother Classes "Copula", etc of all Copulas in
                            the Package
    copula-package          Multivariate Dependence Modeling with Copulas
    corKendall              (Fast) Computation of Pairwise Kendall's Taus
    dDiag                   Density of the Diagonal of (Nested) Archimedean
                            Copulas
    describeCop             Copula (Short) Description as String
    dnacopula               Density Evaluation for (Nested) Archimedean
                            Copulas
    ebeta                   Various Estimators for (Nested) Archimedean
                            Copulas
    ellipCopula             Construction of Elliptical Copula Class Objects
    ellipCopula-class       Class "ellipCopula" of Elliptical Copulas
    emde                    Minimum Distance Estimators for (Nested)
                            Archimedean Copulas
    emle                    Maximum Likelihood Estimators for (Nested)
                            Archimedean Copulas
    empCopula               The Empirical Copula
    empCopula-class         Class "empCopula" of Empirical Copulas
    enacopula               Estimation Procedures for (Nested) Archimedean
                            Copulas
    evCopula                Construction of Extreme-Value Copula Objects
    evCopula-class          Classes Representing Extreme-Value Copulas
    evTestA                 Bivariate Test of Extreme-Value Dependence
                            Based on Pickands' Dependence Function
    evTestC                 Large-sample Test of Multivariate Extreme-Value
                            Dependence
    evTestK                 Bivariate Test of Extreme-Value Dependence
                            Based on Kendall's Distribution
    exchEVTest              Test of Exchangeability for Certain Bivariate
                            Copulas
    exchTest                Test of Exchangeability for a Bivariate Copula
    fgmCopula               Construction of a fgmCopula Class Object
    fgmCopula-class         Class "fgmCopula" - Multivariate Multiparameter
                            Farlie-Gumbel-Morgenstern Copulas
    fhCopula                Construction of Fréchet-Hoeffding Bound Copula
                            Objects
    fhCopula-class          Class "fhCopula" of Fréchet-Hoeffding Bound
                            Copulas
    fitCopula               Fitting Copulas to Data - Copula Parameter
                            Estimation
    fitCopula-class         Classes of Fitted Multivariate Models: Copula,
                            Mvdc
    fitLambda               Non-parametric Estimators of the Matrix of
                            Tail-Dependence Coefficients
    fitMvdc                 Estimation of Multivariate Models Defined via
                            Copulas
    fixParam                Fix a Subset of a Copula Parameter Vector
    gasoil                  Daily Crude Oil and Natural Gas Prices from
                            2003 to 2006
    getAcop                 Get "acopula" Family Object by Name
    getIniParam             Get Initial Parameter Estimate for Copula
    getTheta                Get the Parameter(s) of a Copula
    gnacopula               Goodness-of-fit Testing for (Nested)
                            Archimedean Copulas
    gofBTstat               Various Goodness-of-fit Test Statistics
    gofCopula               Goodness-of-fit Tests for Copulas
    gofEVCopula             Goodness-of-fit Tests for Bivariate
                            Extreme-Value Copulas
    gofTstat                Goodness-of-fit Test Statistics
    htrafo                  GOF Testing Transformation of Hering and Hofert
    iPsi                    Generator Functions for Archimedean and
                            Extreme-Value Copulas
    indepCopula             Construction of Independence Copula Objects
    indepCopula-class       Class "indepCopula"
    indepTest               Test Independence of Continuous Random
                            Variables via Empirical Copula
    initOpt                 Initial Interval or Value for Parameter
                            Estimation of Archimedean Copulas
    interval                Construct Simple "interval" Object
    interval-class          Class "interval" of Simple Intervals
    khoudrajiCopula         Construction of copulas using Khoudraji's
                            device
    khoudrajiCopula-class   Class '"khoudrajiCopula"' and its Subclasses
    log1mexp                Compute f(a) = log(1 +/- exp(-a)) Numerically
                            Optimally
    loss                    LOSS and ALAE Insurance Data
    margCopula              Marginal copula of a Copula With Specified
                            Margins
    mixCopula               Create Mixture of Copulas
    mixCopula-class         Class '"mixCopula"' of Copula Mixtures
    moCopula                The Marshall-Olkin Copula
    moCopula-class          Class "moCopula" of Marshall-Olkin Copulas
    multIndepTest           Independence Test Among Continuous Random
                            Vectors Based on the Empirical Copula Process
    multSerialIndepTest     Serial Independence Test for Multivariate Time
                            Series via Empirical Copula
    mvdc-class              Class "mvdc": Multivariate Distributions from
                            Copulas
    nacFrail.time           Timing for Sampling Frailties of Nested
                            Archimedean Copulas
    nacPairthetas           Pairwise Thetas of Nested Archimedean Copulas
    nacopula-class          Class "nacopula" of Nested Archimedean Copulas
    nesdepth                Nesting Depth of a Nested Archimedean Copula
                            ("nacopula")
    onacopula               Constructing (Outer) Nested Archimedean Copulas
    opower                  Outer Power Transformation of Archimedean
                            Copulas
    p2P                     Tools to Work with Matrices
    pacR                    Distribution of the Radial Part of an
                            Archimedean Copula
    pairs2                  Scatter-Plot Matrix ('pairs') for Copula
                            Distributions with Nice Defaults
    pairsRosenblatt         Plots for Graphical GOF Test via Pairwise
                            Rosenblatt Transforms
    pairwiseCcop            Computations for Graphical GOF Test via
                            Pairwise Rosenblatt Transforms
    persp-methods           Methods for Function 'persp' in Package
                            'copula'
    plackettCopula          Construction of a Plackett Copula
    plackettCopula-class    Class "plackettCopula" of Plackett Copulas
    plot-methods            Methods for 'plot' in Package 'copula'
    pnacopula               Evaluation of (Nested) Archimedean Copulas
    pobs                    Pseudo-Observations
    polylog                 Polylogarithm Li_s(z) and Debye Functions
    polynEval               Evaluate Polynomials
    printNacopula           Print Compact Overview of a Nested Archimedean
                            Copula ("nacopula")
    prob                    Computing Probabilities of Hypercubes
    qqplot2                 Q-Q Plot with Rugs and Pointwise Asymptotic
                            Confidence Intervals
    rAntitheticVariates     Variance-Reduction Methods
    rF01Frank               Sample Univariate Distributions Involved in
                            Nested Frank and Joe Copulas
    rFFrank                 Sampling Distribution F for Frank and Joe
    radSymTest              Test of Exchangeability for a Bivariate Copula
    rdj                     Daily Returns of Three Stocks in the Dow Jones
    retstable               Sampling Exponentially Tilted Stable
                            Distributions
    rlog                    Sampling Logarithmic Distributions
    rnacModel               Random nacopula Model
    rnacopula               Sampling Nested Archimedean Copulas
    rnchild                 Sampling Child 'nacopula's
    rotCopula               Construction and Class of Rotated aka Reflected
                            Copulas
    rstable1                Random numbers from (Skew) Stable Distributions
    safeUroot               One-dimensional Root (Zero) Finding - Extra
                            "Safety" for Convenience
    serialIndepTest         Serial Independence Test for Continuous Time
                            Series Via Empirical Copula
    setTheta                Specify the Parameter(s) of a Copula
    show-methods            Methods for 'show()' in Package 'copula'
    splom2-methods          Methods for Scatter Plot Matrix 'splom2' in
                            Package 'copula'
    tau                     Dependence Measures for Bivariate Copulas
    tauAMH                  Ali-Mikhail-Haq ("AMH")'s and Joe's Kendall's
                            Tau
    uranium                 Uranium Exploration Dataset of Cook & Johnson
                            (1986)
    wireframe2-methods      Perspective Plots - 'wireframe2' in Package
                            'copula'
    xvCopula                Model (copula) selection based on 'k'-fold
                            cross-validation

Further information is available in the following vignettes:

`AC_Liouville` | Archimedean Liouville Copulas (source)
`AR_Clayton` | MLE and Quantile Evaluation for a Clayton AR(1) Model with Student Marginals (source)
`GIG` | Generalized Inverse Gaussian Archimedean Copulas (source)
`HAXC` | Hierarchical Archimax Copulas (source)
`NALC` | Nested Archimedean Lévy Copulas (source)
`copula_GARCH` | The Copula GARCH Model (source)
`dNAC` | Densities of Two-Level Nested Archimedean Copulas (source)
`empiricial_copulas` | Exploring Empirical Copulas (source)
`logL_visualization` | Log-Likelihood Visualization for Archimedean Copulas (source)
`qrng` | Quasi-Random Numbers for Copula Models (source)
`wild_animals` | Wild Animals: Examples of Nonstandard Copulas (source)
`Frank-Rmpfr` | Numerically stable Frank Copulas via Multiprecision (Rmpfr) (source)
`nacopula-pkg` | Nested Archimedean Copulas Meet R (source)
`rhoAMH-dilog` | Beautiful Spearman's Rho for AMH Copula (source)

The copula package provides

- Classes (S4) of commonly used copulas including elliptical (normal and t; `ellipCopula`), Archimedean (Clayton, Gumbel, Frank, Joe, and Ali-Mikhail-Haq; ; `archmCopula` and `acopula`), extreme value (Gumbel, Husler-Reiss, Galambos, Tawn, and t-EV; `evCopula`), and other families (Plackett and Farlie-Gumbel-Morgenstern).

- Methods for density, distribution, random number generation (`dCopula`, `pCopula` and `rCopula`); bivariate dependence measures (`rho`, `tau`, etc), perspective and contour plots.

- Functions (and methods) for fitting copula models including variance estimates (`fitCopula`).

- Independence tests among random variables and vectors.

- Serial independence tests for univariate and multivariate continuous time series.

- Goodness-of-fit tests for copulas based on multipliers, and the parametric bootstrap, with several transformation options.

- Bivariate and multivariate tests of extreme-value dependence.

- Bivariate tests of exchangeability.

Now with former package nacopula for working with nested Archimedean copulas. Specifically,

- it provides procedures for computing function values and cube volumes (`prob`),

- characteristics such as Kendall's tau and tail dependence coefficients (via family objects, e.g., `copGumbel`),

- efficient sampling algorithms (`rnacopula`),

- various estimators and goodness-of-fit tests.

- The package also contains related univariate distributions and special functions such as the Sibuya distribution (`Sibuya`), the polylogarithm (`polylog`), Stirling and Eulerian numbers (`Eulerian`).

Further information is available in the following vignettes:

`nacopula-pkg` | Nested Archimedean Copulas Meet R (../doc/nacopula-pkg.pdf)
`Frank-Rmpfr` | Numerically Stable Frank via Multiprecision in R (../doc/Frank-Rmpfr)

For a list of exported functions, use `help(package = "copula")`.

### References

Yan, J. (2007) Enjoy the Joy of Copulas: With a Package copula. Journal of Statistical Software 21(4), 1–21. https://www.jstatsoft.org/v21/i04/.

Kojadinovic, I. and Yan, J. (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software 34(9), 1–20. https://www.jstatsoft.org/v34/i09/.

Hofert, M. and Mächler, M. (2011), Nested Archimedean Copulas Meet R: The nacopula Package., Journal of Statistical Software 39(9), 1–20. https://www.jstatsoft.org/v39/i09/.

Nelsen, R. B. (2006) An introduction to Copulas. Springer, New York.

### See Also

The following CRAN packages currently use (‘depend on’) copula: CoClust, copulaedas, Depela, HAC, ipptoolbox, vines.

### Examples

    ## Some of the more important functions (and their examples) are

    example(fitCopula)## fitting Copulas
    example(fitMvdc)  ## fitting multivariate distributions via Copulas
    example(nacopula) ## nested Archimedean Copulas

    ## Independence Tests:  These also draw a 'Dependogram':
    example(indepTest)       ## Testing for Independence
    example(serialIndepTest) ## Testing for Serial Independence

[Package copula version 1.0-1 Index]