Generalized Additive Models for Bivariate Conditional Dependence Structures and Vine Copulas • gamCopula

This R package implements the generalized additive modeling framework for bivariate copulas introduced by Vatter and Chavez-Demoulin (2015) and its extension to Pair-Copula Constructions (or Vine Copulas) by Vatter and Nagler (2017). It includes functions for parameter estimation, model selection, simulation, and visualization. The package is still under development. Please see the API documentation for a detailed description of all functions.

How to install
Package overview
References

How to install

You can install:

the stable release on CRAN:
```
install.packages("gamCopula")
```

the latest development version:

devtools::install_github("tvatter/gamCopula")

Package overview

Below, we list most functions and features you should know about. As usual in copula models, data are assumed to be serially independent and lie in the unit hypercube.

Bivariate copula modeling: the gamBiCop-class

gamBiCop: Creates a GAM bivariate copula by specifying a family and model, namely a gamObject as return by the gam function from the mgcv package. Returns an object of class gamBiCop. The class has the following methods:
- print, summary: a brief or comprehensive overview of the bivariate copula, respectively.
- plot: plot method based on plot.gam from mgcv.
- logLik, AIC, BIC, nobs: usual fit statistics.
- EDF: Equivalent degrees of freedom for the components of the model.
gamBiCopSimulate: Simulates from a bivariate GAM copula.
gamBiCopFit: Estimates parameters of a bivariate copula with a prespecified family. Returns an object of class gamBiCop.
gamBiCopSelect: Estimates the parameters of a bivariate copula for a set of families and selects the best fitting model (using either AIC or BIC). Returns an object of class gamBiCop.
gamBiCopPredict, gamBiCopPDF, gamBiCopCDF: Predict and PDF/CDF methods for the GAM copula model.

Vine copula modeling: the gamVine-class

gamVine: Creates a GAM vine copula model by specifying a tree structure and list of gamBicop objects corresponding to each edge. Returns an object of class gamVine. The class has the following methods:
- print, summary: a brief or comprehensive overview of the bivariate copula, respectively.
- plot: plots based on plot.gamBiCop.
gamVineSimulate: Simulates from a GAM vine copula model.
gamVineSeqFit: Estimates the parameters of a GAM vine copula model with prespecified structure and families.
gamVineCopSelect: Estimates the parameters and selects the best family for a GAM vine copula model with prespecified structure matrix.
gamVineStructureSelect: Fits a GAM vine copula model assuming no prior knowledge. It selects the R-vine structure using Dissmann et al. (2013)’s method, estimates parameters for various families, and selects the best family for each pair.
gamVinePDF: Computes the PDF for a given gamVine object.
RVM2GVC: converts an RVineMatrix object from the VineCopula package into a gamVine

Bivariate copula families

In this package several bivariate copula families are included for bivariate and multivariate analysis using vine copulas. It provides functionality of elliptical (Gaussian and Student-t) as well as Archimedean (Clayton, Gumbel, Frank) copulas to cover a large range of dependence patterns. For the Clayton and Gumbel copula families, rotated versions are included to cover negative dependence as well.

A copula family: 1 Gaussian, 2 Student t, 5 Frank, 301 Double Clayton type I (standard and rotated 90 degrees), 302 Double Clayton type II (standard and rotated 270 degrees), 303 Double Clayton type III (survival and rotated 90 degrees), 304 Double Clayton type IV (survival and rotated 270 degrees), 401 Double Gumbel type I (standard and rotated 90 degrees), 402 Double Gumbel type II (standard and rotated 270 degrees), 403 Double Gumbel type III (survival and rotated 90 degrees), 404 Double Gumbel type IV (survival and rotated 270 degrees).

The following table shows the parameter ranges of bivariate copula families with parameters par and par2 and internal coding family:

Copula family	`family`	`par`	`par2`
Gaussian	`1`	`(-1, 1)`	-
Student t	`2`	`(-1, 1)`	`(2,Inf)`
Double Clayton type I (standard and 90 degrees)	`301`	`(-Inf, Inf)`	-
Double Clayton type II (standard and 270 degrees)	`302`	`(-Inf, Inf)`	-
Double Clayton type III (survival and 90 degrees)	`303`	`(-Inf, Inf)`	-
Double Clayton type IV (survival and 270 degrees)	`304`	`(-Inf, Inf)`	-
Double Gumbel type I (standard and 90 degrees)	`401`	`(-Inf, Inf)`	-
Double Gumbel type II (standard and 270 degrees)	`402`	`(-Inf, Inf)`	-
Double Gumbel type III (survival and 90 degrees)	`403`	`(-Inf, Inf)`	-
Double Gumbel type IV (survival and 270 degrees)	`404`	`(-Inf, Inf)`	-
Frank	`5`	`R \ {0}`	-

References

Vatter, T., Nagler, T. (2017)
Generalized Additive Models for Pair-Copula Constructions.
Preprint available at arXiv:1608.01593.

Vatter, T., Chavez-Demoulin, V. (2015).
Generalized additive models for conditional dependence structures.
Journal of Multivariate Analysis, 141: 147-167, http://dx.doi.org/10.1016/j.jmva.2015.07.003.