This package provides functionality to estimate, analyze and simulate bivariate and multivariate copula models. At its core most bivariate functionality currently is built upon the VineCopulaCPP C++ package of Malte Kurz. Multivariate extensions to pair copula constructions (vine copulas) are mostly implemented in native Julia code.
You can access the documentation here.
As the package makes use of the VineCopulaCPP C++ package, it also shares the same requirements to some further libraries. On Ubuntu 14.04 they can easily be installed with the following commands:
sudo apt-get -y install libboost-all-dev
sudo apt-get -y install libnlopt-dev
sudo apt-get -y install libgomp1
For some linux distributions there might be no nlopt
library available
through the official package repository. In this case, simply download
the package directly from the nlopt webpage. For additional resources
for the installation of additional requirements take a look at the
.travis.yml file in the package's repository.
Once that you have installed all software dependencies, you need to
compile the underlying C++ library. Therefore, the C++ source code is
added to the repository as a git submodule residing in
/src/VineCopulaCPP. In order to directly get the source code
together with the repository, you can clone both with command
git clone --recursive https://github.com/JuliaFinMetriX/Copulas.jl.git
Alternatively, the package also comes with a Makefile that does the
job for you. In the package directory, simply type
make
Calling make will cause VineCopulaCPP to download the MVTDST
Fortran
90
library of Alan Genz. In order to correctly compile this library you
also need a fortran compiler, e.g. gfortran.
Copulas currently calls C++ code, which is not yet natively
supported by Julia. C++ code can be called through Julia's built-in
functionality for C code, but still needs to take into account some
additional name
mangling. In other words,
calling function PairCopulaPDF in C++ requires to adapt the function
name with pre- and suffix which depend on input and output types of
the function, but should also be system dependent. For example,
PairCopulaPDF must be called as _Z13PairCopulaPDFiPKdPdS1_S1_j on
Ubuntu 14.04.
These modified names are specified in
/src/ParamPCs_Cpp/ParamPC_Cpp.jl. If they do not work for you,
simply adapt them to your needs. In order the get the names on your
system, call
nm -D /src/VineCopulaCPP/libVineCPP.so.1.0
to list all functions with mangled names and adapt them accordingly in
/src/ParamPCs_Cpp/ParamPC_Cpp.jl.
For details on the underlying copula theory take a look at my research notes.
In its current version, Copulas.jl basically is only a wrapper to
the fabulous
VineCopulaCPP c++
library of Malte Kurz. VineCopulaCPP
is a well tested library comprising parametric copulas with all
their respective functions (pdf, cdf,...), as well as simulation
routines and optimization algorithms for copula estimation.