VineCopula (version 2.6.1)

RVinePIT: Probability Integral Transformation for R-Vine Copula Models

Description

This function applies the probability integral transformation (PIT) for R-vine copula models to given copula data.

Usage

RVinePIT(data, RVM)

Value

An N x d matrix of PIT data from the given R-vine copula model.

Arguments

data

An N x d data matrix (with uniform margins).

RVM

RVineMatrix() objects of the R-vine model.

Author

Ulf Schepsmeier

Details

The multivariate probability integral transformation (PIT) of Rosenblatt (1952) transforms the copula data $u=(u_1,\dots ,u_d)$ with a given multivariate copula C into independent data in $[0,1{]}^d$, where d is the dimension of the data set.

Let $u=(u_1,\dots ,u_d)$ denote copula data of dimension d. Further let C be the joint cdf of $u=(u_1,\dots ,u_d)$. Then Rosenblatt's transformation of u, denoted as $y=(y_1,\dots ,y_d)$, is defined as $$y_1:=u_1,y_2:=C(u_2|u_1),\dots y_d:=C(u_d|u_1,\dots ,u_{d-1}),$$ where $C(u_k|u_1,\dots ,u_{k-1})$ is the conditional copula of $U_k$ given $U_1=u_1,\dots ,U_{k-1}=u_{k-1},k=2,\dots ,d$. The data vector $y=(y_1,\dots ,y_d)$ is now i.i.d. with $y_i\sim U[0,1]$. The algorithm for the R-vine PIT is given in the appendix of Schepsmeier (2015).

References

Rosenblatt, M. (1952). Remarks on a Multivariate Transformation. The Annals of Mathematical Statistics 23 (3), 470-472.

Schepsmeier, U. (2015) Efficient information based goodness-of-fit tests for vine copula models with fixed margins. Journal of Multivariate Analysis 138, 34-52.

See Also

RVineGofTest()

Examples

# load data set
data(daxreturns)

# select the R-vine structure, families and parameters
RVM <- RVineStructureSelect(daxreturns[,1:3], c(1:6))

# PIT data
pit <- RVinePIT(daxreturns[,1:3], RVM)

par(mfrow = c(1,2))
plot(daxreturns[,1], daxreturns[,2])	# correlated data
plot(pit[,1], pit[,2])	# i.i.d. data

cor(pit, method = "kendall")