kn {npcopTest}

Estimation of the location of the change point in the copula

Description

Give an estimation of the abrupt change point in the copula when changes known occurs in the m.c.d.f.

Usage

kn(X,b)

Arguments

X

a (non-empty) numeric matrix of d-dimensional data values, d\geq 2. Each row of the matrix contains one mutlivariate data.

b

a single value or a vector of real values on (0,1] indicating the location(s) of the potential break time(s) in marginal cumulative distribution functions. You can specify b=1 (default) for any break time.

Details

Estimation of the location of the abrupt change point in copula

Value

estimation of the location of the change point in the copula

Author(s)

Rohmer Tom

References

Tom Rohmer, Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributions, Statistics & Probability Letters, Volume 119, December 2016, Pages 45-54, ISSN 0167-7152

Examples

#Example 1: Abrupt change in the m.c.d.f at time (known) m=50 
# and in the copula at time k=50 (to be estimated)
n=100
m=50
mean1 = rep(0,2)
mean2 = rep(4,2)
sigma1 = matrix(c(1,0.2,0.2,1),2,2)
sigma2 = matrix(c(1,0.6,0.6,1),2,2)

X=matrix(rep(0,n*2),n,2)
for(j in 1:m) X[j,]=t(chol(sigma1))%*%rnorm(2) + mean1
for(j in (m+1):n) X[j,]=t(chol(sigma2))%*%rnorm(2) + mean2

kn(X,b=0.5) 


#Example 2: Abrupt changes in the m.c.d.f at times (known) m=100 and 150
# and in the copula at time k=50 (to be estimated)
n=200
m1 = 100
m2 = 150
k = 50

sigma1 = matrix(c(1,0.2,0.2,1),2,2)
sigma2 = matrix(c(1,0.6,0.6,1),2,2)

mean1 = rep(0,2)
mean2 = rep(2,2)
mean3 = rep(4,2)

X=matrix(rep(0,n*2),n,2)
for(j in 1:k) X[j,]=t(chol(sigma1))%*%rnorm(2)
for(j in (k+1):n) X[j,]=t(chol(sigma2))%*%rnorm(2)

X[1:m1,]=X[1:m1,]+mean1
X[(m1+1):m2,]=X[(m1+1):m2,]+mean2
X[(m2+1):n,]=X[(m2+1):n,]+mean3

kn(X,b=c(0.5,0.75))