cpRho  R Documentation 
Nonparametric test for changepoint detection particularly sensitive to changes in Spearman's rho in multivariate time series. The observations can be serially independent or dependent (strongly mixing). Approximate pvalues for the test statistic are obtained by means of a multiplier approach or by estimating the asymptotic null distribution. Details can be found in first reference.
cpRho(x, method = c("mult", "asym.var"), statistic = c("pairwise", "global"), b = NULL, weights = c("parzen", "bartlett"), N = 1000, init.seq = NULL, include.replicates = FALSE)
x 
a data matrix whose rows are multivariate continuous observations. 
method 
a string specifying the method for computing the
approximate pvalue for the test statistic; can be either

statistic 
a string specifying 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. 
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 
When method == "mult"
, 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.
When method == "asym.var"
, the approximate pvalue is computed
from the estimated asymptotic null distribution, which involves the
Kolmogorov distribution. The latter is dealt with reusing code from
the ks.test()
function; credit to RCore.
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. 
rho 
the values of the 
b 
the value of parameter 
These tests were derived under the assumption of continuous margins.
I. Kojadinovic, JF. Quessy and T. Rohmer (2016), Testing the constancy of Spearman's rho in multivariate time series, Annals of the Institute of Statistical Mathematics 68:5, pages 929954, https://arxiv.org/abs/1407.1624.
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.
cpTau()
for a related test based on
Kendall's tau, cpDist()
for a related test
based on the multivariate
empirical d.f., cpCopula()
for a related test based on
the empirical copula.
## Not run: require(copula) n < 100 k < 50 ## the true changepoint u < rCopula(k,gumbelCopula(1.5)) v < rCopula(nk,gumbelCopula(3)) x < rbind(u,v) cp < cpRho(x, b = 1) cp ## Estimated changepoint which(cp$rho == max(cp$rho)) ## End(Not run)
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