| Title: | Non-Central Squared Copula Models Estimation |
| Version: | 1.0.1 |
| Author: | Bouchra R. Nasri |
| Maintainer: | Bouchra R. Nasri <bouchra.nasri@gmail.com> |
| Description: | Inference and dependence measure for the non-central squared Gaussian, Student, Clayton, Gumbel, and Frank copula models.The description of the methodology is taken from Section 3 of Nasri, Remillard and Bouezmarni (2019) <doi:10.1016/j.jmva.2019.03.007>. |
| Depends: | copula |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.0.0 |
| NeedsCompilation: | no |
| Packaged: | 2019-11-22 19:37:52 UTC; Utilisateur |
| Repository: | CRAN |
| Date/Publication: | 2019-11-28 16:50:02 UTC |
Estimation of a non-central squared copula model
Description
This function estimates the copula parameter and the non-centrality parameters of a non-central squared copula
Usage
EstNCSCop(y, family, p = 2, InitialValues = NULL)
Arguments
y |
(nx2) data matrix (observations or residuals) that will be transformed to pseudo-observations |
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel' |
p |
number of non-centrality parameters to be estimated (p = 0,1,2) |
InitialValues |
initial values c(a1,a2,tau) to start the estimation; otherwise pre-selected values will be used |
Value
theta |
Estimated parameter of the copula according to CRAN copula package |
dof |
Estimated degrees of freedom, only for the Student copula |
tau |
Estimated theoretical Kendall tau for the copula family |
Author(s)
Bouchra R. Nasri, August 14, 2019
References
Section 5.1 of Nasri, Rémillard & Bouezmarni (2019). Semi-parametric copula-based models under non-stationarity, Journal of Multivariate Analysis, 173, pages 347-365.
Examples
param <- c(0.8, 2.5, 0.7) ;
U <- SimNCSCop('Clayton', 250, param)
estimation <- EstNCSCop(U,'Clayton')
Kendall's tau of a copula
Description
This function computes the Kendall's tau of a copula family for a given a unconstrainted parameter alpha.
Usage
KendallTau(family, alpha)
Arguments
family |
"Gaussian" , "t" , "Clayton" , "Frank" , "Gumbel" |
alpha |
unconstrainted parameters of the copula family |
Value
tau |
estimated Kendall's tau |
theta |
estimated copula parameter (constrained) |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
KendallTau('Clayton',0)
Log-likelihood of a non-central squared copula
Description
This function computes the log-likelihood vector of a non-central squared copula
Usage
LoglikNCSCop(alpha, U, family, p = 2)
Arguments
alpha |
unconstrained non-centrality parameters a1, a2, and unconstrained copula parameters. |
U |
(nx2) data matrix of pseudo-observations. |
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel'. |
p |
number of different non-centrality parameters (0,1,2 default). |
Value
LL |
Vector of log-likelihoods |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
alpha = c(log(0.2),log(5),log(2),log(12));
param = c(0.5,2.5,0.5);
data = SimNCSCop('Clayton', 250, param);
LL = LoglikNCSCop(alpha,data,'Clayton')
Distribution function of a non-central squared copula
Description
This function computes the distribution function a non-central squared copula
Usage
NCSCopCdf(u, family, param, dof = NULL)
Arguments
u |
(nx2) data matrix of pseudo-observations. |
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel'. |
param |
c(a1,a2,tau) where a1,a2 are the non-negative non-centrality |
dof |
degrees of freedom of the Student copula (if needed). |
Value
cdf |
Non-central squared copula evaluated at points u. |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
param = c(0.8,2.5,0.7);
u = matrix(c(0.2,0.6,0.3,0.5,0.7,0.9),ncol=2,byrow=TRUE);
cdf=NCSCopCdf(u,'Clayton',param);
Gives the parameters of the copula family
Description
This function computes the parameter of the copula according to CRAN copula package where corresponding to the unconstrainted parameters alpha.
Usage
ParamCop(family, alpha)
Arguments
family |
"Gaussian" , "t" , "Clayton" , "Frank" , "Gumbel" |
alpha |
unconstrainted parameters of the copula family |
Value
theta |
Bivariate vector of constrained copula family parameters |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
ParamCop('Clayton',0)
Unconstrained parameters
Description
This function computes the unconstrainted parameter alpha for a given Kendall's tau
Usage
ParamTau(family, tau)
Arguments
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel' |
tau |
Kendall's tau of the copula family |
Value
alpha |
Unconstrainted parameter |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
ParamTau('Clayton',0.5)
Simulation of a bivariate non-central squared copula
Description
This function simulates observations a bivariate non-central squared copula model.
Usage
SimNCSCop(family, n, param, DoF = NULL)
Arguments
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel'. |
n |
number of simulated vectors. |
param |
c(a1,a2,tau) where a1,a2 are the non-negative non-centrality |
DoF |
degrees of freedom of the Student copula (if needed). |
Value
U |
Simulated Data |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
param <- c(0.8, 2.5, 0.7) ;
U <- SimNCSCop('Clayton', 250, param)
Empirical copula
Description
This function computes the empirical bivariate copula at a series of points.
Usage
copulaEmp(u, U)
Arguments
u |
(nx2) data matrix of points. |
U |
(nx2) data matrix of pseudo-observations. |
Value
cdf |
Empirical copula values at u. |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
param <- c(0.8, 2.5, 0.7) ;
U <- SimNCSCop('Clayton', 250, param)
u = matrix(c(0.2,0.6,0.3,0.5,0.7,0.9),ncol=2,byrow=TRUE);
cdf=copulaEmp(u,U);
Initial values for estimation
Description
This function computes initial values of non-centrality parameters and Kendall's tau at selected points for the estimation non-central squared copula parameters. The results are not satisfactory. Do not use.
Usage
initialValues(U, family = "Clayton")
Arguments
U |
(nx2) data matrix of pseudo-observations. |
family |
'Gaussian' , 't' , 'Clayton' , 'Frank' , 'Gumbel'. |
Value
paraml |
Initial values for the non-centrality parameters and Kendall's tau to be included in the EstNCSCop function. |
Author(s)
Bouchra R. Nasri, August 14, 2019
Examples
param <- c(0.8, 2.5, 0.7) ;
U <- SimNCSCop('Clayton', 250, param)
param = initialValues(U, 'Clayton');