Covariate-dependent copula models

Copyright

Feng Li  <feng.li@cufe.edu.cn>
School of Statistics and Mathematics
Central University of Finance and Economics
http://feng.li/

Cite the package

• Li, F., and Kang, Y.(2018). Improving forecasting performance using covariate-dependent copula models, International Journal of Forecasting, 34(3), pp. 456-476.

Prerequisites

Environment requirements

• git tools (for downloading the library)

• R > 3.0.0 with the following required packages:

  • devtools

  • mvtnorm Rmfpr numDeriv optimix

  • rugarch rmgarch fGarch stochvol teigen

  • VineCopula

  • snow, Rmpi (optional)

Installation

The package is currently under developments. We are not yet ready to make it as a standard R package. Please follow the following instructions to "load" the functionality.

Clone the repository and its dependencies

• This package depends on flutils package. Install it with devtools

devtools::install_github("feng-li/flutils")

devtools::install_github("feng-li/cdcopula")

Run a covariate-dependent copula model

• The example model configuration files are located at inst/config/.

• Linux executable scripts are provided at inst/bin/. For more information, you may issue the following command in a terminal

inst/bin/CplRun --help

• Or within R, use

library("cdcopula")
CplRun(Mdl.ConfigFile=file.path(system.file(package = "cdcopula"), 'config/config.BB7.GARCH.SP100-SP600.R'))

Cluster Parallelization

• Run with SLURM cluster

mpirun -np 1  inst/bin/CplRun 4 inst/config/${CONFIG_FILE}

And submit to slurm with

sbatch inst/config/slurm.sh

Implementing a new covariate-dependent copula model

First you may need to consult the reference paper. Then you could edit the following files accordingly.

for the copula model

• pCpl.R, dCpl.R Copula functions and their densities.

• logCplGrad.R Gradient function for log copula density w.r.t. copula parameters.

• logCplRepGrad.R Gradient function for reparameterized log copula density w.r.t. copula parameters which may require

  • parCplRep2Std.R

  • kendalltau.R, kendalltauGrad.R

  • lambda.R, lambdaGrad.R

for the marginal model

• If you want to implement a native marginal model edit the following files

  • MargiModel.R CDF and PDF of the marginal distribution

  • MargiModelGrad.R Gradient for CDF and PDF of the marginal distribution

  • MargiModelInv.R The inverse for marginal model

• If you want to include a foreign marginal model with existing algorithms, edit the following files

  • MargiModelForeignEval.R

  • MargiModelForeignPred.R

  • logCplPredict.R

• If you want to include a foreign multivariate model for model comparison, edit the following files

  • ModelForeignEval.R

  • ModelForeignPred.R

References

• Li, F., Panagiotelis, A. and Kang, Y. (2019) Modelling multivariate tail-dependence with covariate-dependent vine copulas, Working paper.

• Li, F., and Kang, Y.(2018). Improving forecasting performance using covariate-dependent copula models, International Journal of Forecasting, 34(3), pp. 456-476.

Acknowledgments

Feng Li's research were supported by the National Natural Science Foundation of China (No. 11501587).