cpCopula  R Documentation 
Nonparametric test for changepoint detection particularly sensitive to changes in the copula of multivariate continuous observations. The observations can be serially independent or dependent (strongly mixing). Approximate pvalues for the test statistic are obtained by means of a multiplier approach. Details can be found in the first reference.
cpCopula(x, method = c("seq", "nonseq"), b = NULL, weights = c("parzen", "bartlett"), m = 5, L.method=c("max","median","mean","min"), N = 1000, init.seq = NULL, include.replicates = FALSE)
x 
a data matrix whose rows are multivariate continuous observations. 
method 
a string specifying the simulation method for
generating multiplier replicates of the test statistic;
can be either 
b 
strictly positive integer specifying the value of the
bandwidth parameter determining the serial dependence when
generating dependent multiplier sequences using the 'moving average
approach'; see Section 5 of the second reference. The
value 1 will create i.i.d. multiplier
sequences suitable for serially independent observations. If set to

weights 
a string specifying the kernel for creating the weights used in the generation of dependent multiplier sequences within the 'moving average approach'; see Section 5 of the second reference. 
m 
a strictly positive integer specifying the number of points of the
uniform grid on (0,1)^d (where d is

L.method 
a string specifying how the parameter L involved in the estimation of the bandwidth parameter is computed; see Section 5 of the second reference. 
N 
number of multiplier replications. 
init.seq 
a sequence of independent standard normal variates of
length 
include.replicates 
a logical specifying whether the
object of 
The approximate pvalue is computed as
(0.5 + sum(S[i] >= S, i=1, .., N)) / (N+1),
where S and S[i] denote the test statistic and a multiplier replication, respectively. This ensures that the approximate pvalue is a number strictly between 0 and 1, which is sometimes necessary for further treatments.
An object of class
htest
which is a list,
some of the components of which are
statistic 
value of the test statistic. 
p.value 
corresponding approximate pvalue. 
cvm 
the values of the 
b 
the value of parameter 
These tests were derived under the assumption of continuous margins.
A. Bücher, I. Kojadinovic, T. Rohmer and J. Segers (2014), Detecting changes in crosssectional dependence in multivariate time series, Journal of Multivariate Analysis 132, pages 111128, https://arxiv.org/abs/1206.2557.
A. Bücher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927968, https://arxiv.org/abs/1306.3930.
cpRho()
for a related test based on
Spearman's rho, cpTau()
for a related test based on
Kendall's tau, cpDist()
for a related test based
on the multivariate empirical d.f., bOptEmpProc()
for the
function used to estimate b
from x
if b = NULL
.
## Not run: require(copula) n < 100 k < 50 ## the true changepoint u < rCopula(k, gumbelCopula(1.5)) v < rCopula(n  k, gumbelCopula(3)) x < rbind(u,v) cp < cpCopula(x, b = 1) cp ## Estimated changepoint which(cp$cvm == max(cp$cvm)) ## End(Not run)
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