boostCopula: Gradient-Boosted Estimation of Generalized Linear Models for Conditional Vine Copulas

An R package performing gradient-boosting estimation of generalized linear models (GLMs) for conditional vine copulas as described in the references.

Installation

You can install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("jobstdavid/boostCopula")

Package overview

Overview of the most important functions

• boostBiCopEst: This function estimates a GLM for a conditional bivariate copula via gradient-boosting. It returns an object of class boostBiCop.
• boostBiCopSelect: This function performs a gradient-boosted estimation of a GLM for conditional bivariate copulas including copula family selection. It returns an object of class boostBiCop.
• boostBiCopPDF, boostBiCopCDF: These function calculate the probability density function (PDF) or cumulative distribution function (CDF) of an boostBiCop object, respectively.
• boostBiCopSim: This function simulates samples from an boostBiCop object.
• boostRVineSeqEst: This function sequentially estimates the GLMs for conditional bivariate copulas of a d-dimensional conditional R-vine copula model via gradient-boosting. It returns an object of class boostRVineCopula.
• boostRVineCopSelect: This function sequentially estimates the GLMs for conditional bivariate copulas of a d-dimensional conditional R-vine copula model via gradient-boosting. Additionally, it selects the best fitting copula family. It returns an object of class boostRVineCopula.
• boostRVineStructureSelect: This function sequentially selects the regular vine tree structure as well as the conditional bivariate copulas via a gradient-boosted estimation of GLMs for a d-dimensional conditional R-vine copula model. It returns an object of class boostRVineCopula.
• boostRVinePDF: This function calculates the probability density function (PDF) of an boostRVineCopula object.
• boostRVineSim: This function simulates samples from an boostRVineCopula object.

Overview of the implemented copula families

Copula family	family
Gaussian	1
Double Clayton I copula (0 and 90 degrees)	301
Double Clayton II copula (0 and 270 degrees)	302
Double Clayton III copula (180 and 90 degrees)	303
Double Clayton IV copula (180 and 270 degrees)	304
Double Gumbel I copula (0 and 90 degrees)	401
Double Gumbel II copula (0 and 270 degrees)	402
Double Gumbel III copula (180 and 90 degrees)	403
Double Gumbel IV copula (180 and 270 degrees)	404

Example

Load R-package and simulated data

# load package
library(boostCopula)

# load simulated data
data(data_bicop)
data(data_vinecop)

Gradient-boosted estimation of a GLM for a conditional bivariate copula

# fit object
object <- boostBiCopEst(formula = ~.,
                        U = data_bicop[, 1:2],
                        X = data_bicop[, -c(1:2)],
                        family = 301,
                        control = boost_control(deselection = "attributable"))
summary(object)
#> Conditional bivariate copula: double Clayton I (301)
#> Non-zero coefficients:
#> (Intercept)           X1           X2           X3           X4           X5  
#>      0.0925      -0.1565       0.2675       0.2124       0.4953      -0.3883  
#> 
#> logLik: 499.804, AIC: -987.608, degrees of freedom: 6
#> Iterations: 65
plot(object)

Gradient-boosted estimation of a GLM for conditional bivariate copulas including copula family selection

# fit object
object <- boostBiCopSelect(formula = ~.,
                           U = data_bicop[, 1:2],
                           X = data_bicop[, -c(1:2)],
                           familyset = NA,
                           control = boost_control(deselection = "attributable"))
summary(object)
#> Conditional bivariate copula: double Clayton I (301)
#> Non-zero coefficients:
#> (Intercept)           X1           X2           X3           X4           X5  
#>      0.0925      -0.1565       0.2675       0.2124       0.4953      -0.3883  
#> 
#> logLik: 499.804, AIC: -987.608, degrees of freedom: 6
#> Iterations: 65

Sequential gradient-boosted estimation of GLMs for a conditional R-vine copula model

# create boostRVineMatrix
Matrix <- c(5, 0, 0, 0, 0,
            2, 2, 0, 0, 0,
            3, 3, 3, 0, 0,
            1, 4, 4, 4, 0,
            4, 1, 1, 1, 1)
Family <- c(0, 0, 0, 0, 0,
            404, 0, 0, 0, 0,
            1, 404, 0, 0, 0,
            401, 301, 304, 0, 0,
            1, 401, 304, 301, 0)
Matrix <- matrix(Matrix, 5, 5, byrow = TRUE)
Family <- matrix(Family, nrow = 5, ncol = 5, byrow = TRUE)
Formula <- matrix("~ .", 5, 5, byrow = TRUE)
boostRVM <- boostRVineMatrix(Matrix = Matrix,
                             family = Family,
                             formula = Formula)

# fit object
object <- boostRVineSeqEst(U = data_vinecop[, 1:5],
                           X = data_vinecop[, -c(1:5)],
                           boostRVM = boostRVM,
                           control = boost_control(deselection = "attributable"))

Contact

Feel free to contact jobstd@uni-hildesheim.de if you have any questions or suggestions.

References

Jobst, D., Möller, A., and Groß, J. (2024). Gradient-Boosted Generalized Linear Models for Conditional Vine Copulas. doi: 10.48550/arXiv.2406.13500.