README.md

gamCopula

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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.

Table of contents

How to install

You can install:

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

Vine copula modeling: the gamVine-class

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.



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gamCopula documentation built on Aug. 18, 2017, 1:01 a.m.