RVinePIT {VineCopula} | R Documentation |
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)
Arguments
data |
An N x d data matrix (with uniform margins). |
RVM |
|
Details
The multivariate probability integral transformation (PIT) of Rosenblatt
(1952) transforms the copula data with a given
multivariate copula C into independent data in
, where d is the
dimension of the data set.
Let denote copula data of dimension d. Further
let C be the joint cdf of
. Then Rosenblatt's
transformation of u, denoted as
, is defined as
where is the
conditional copula of
given
. The data vector
is now
i.i.d. with
. The algorithm for the R-vine PIT is
given in the appendix of Schepsmeier (2015).
Value
An N
x d matrix of PIT data from the given R-vine copula
model.
Author(s)
Ulf Schepsmeier
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
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")