Description Usage Arguments Details Value Author(s) References Examples

Give the p-value of the test based on the sequential empirical copula process when a break occurs in the marginal cumulative distributions at time m known.

1 | ```
CopTestdm(X,b=1,M=1000)
``` |

`X` |
a (non-empty) numeric matrix of |

`M` |
a strictly positive integer (default |

`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 |

Note that the e.c.d.f.s *F_{k:l,j}* appearing in the construction of pseudo-values (as defined in the section 2 of the first reference) evaluated from the sub-samble *X_{kj},…, X_{lj}* are multiplied by *\frac{l-k+1}{l-k+2}*. Discussions about this subject can be found in the third reference. For serially dependent data, you need to specify dependent multipliers, see the second and third reference for details.

A list with class `htest`

containing the following components:

`m` |
the value of the potential break times in marginal cumulative distribution functions. |

`data.name` |
a character string giving the name of the data. |

`method` |
a character string indicating what type of change-point test was performed. |

`p.value` |
the estimated p-value for the test. |

`statistic` |
the value of the statistic |

Rohmer Tom

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

A. Bucher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927-968

A. Bucher, I. Kojadinovic, T. Rohmer and J. Segers (2014), Detecting changes in cross-sectional dependence in multivariate time series, Journal of Multivariate Analysis 132, pages 111-128

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | ```
#Example 1: under the nulle hypothesis
#of an abrupt change in the m.c.d.f. at time m=50 and no change in the copula
n=100
m=50
sigma = matrix(c(1,0.4,0.4,1),2,2)
mean1 = rep(0,2)
mean2 = rep(4,2)
X=matrix(rep(0,n*2),n,2)
for(j in 1:n) X[j,]=t(chol(sigma))%*%rnorm(2)
X[1:m,] = X[1:m,]+mean1
X[(m+1):n,] = X[(m+1):n,]+mean2
CopTestdm(X,b=0.5)
#Example 2: under the alternative hypothesis
#of an abrupt change in the m.c.d.f at and in the copula time k=m=50
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
CopTestdm(X,b=0.5)
#Example 3: under the alternative hypothesis
#of abrupt changes in the m.c.d.f at times m=100 and 150 and in the copula at time k=50
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
CopTestdm(X,b=c(0.5,0.75))
``` |

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