| empcopsm.test {copula} | R Documentation |
Analog of the serial independence test based on the empirical
copula process proposed by Christian Genest and Bruno
Rémillard (see empcops.test) for multivariate
time series.
The main difference comes from the fact that critical values and
p-values are obtainted through the bootstrap/permutation methodology, since, here,
test statistics are not distribution-free.
empcopsm.test(x, lag.max, m=lag.max+1, N=1000, alpha=0.05)
x |
Data frame or data matrix containing realizations the multivaraite continuous time series whose serial independence is to be tested. |
lag.max |
Maximum lag. |
m |
Maximum cardinality of the subsets of 'lags' for
which a test statistic is to be computed. It makes sense to consider
m << lag.max+1 especially when lag.max is large. |
N |
Number of bootstrap/permutation samples. |
alpha |
Significance level used in the computation of the critical values for the test statistics. |
See the references below for more details, especially the last one.
The function empcopsm.test returns an object of class
empcop.test whose attributes are: subsets,
statistics, critical.values, pvalues,
fisher.pvalue (a p-value resulting from a combination à la
Fisher of the subset statistic p-values), tippett.pvalue (a p-value
resulting from a combination à la Tippett of the subset statistic p-values), alpha (global significance level of the test), beta
(1 - beta is the significance level per statistic),
global.statistic (value of the global Cramér-von Mises
statistic derived directly from
the independence empirical copula process - see In in the last reference) and
global.statistic.pvalue (corresponding p-value).
Ivan Kojadinovic, ivan@stat.auckland.ac.nz
P. Deheuvels (1979), La fonction de dépendance empirique et ses propriétés: un test non paramétrique d'indépendance, Acad. Roy. Belg. Bull. Cl. Sci. 5th Ser. 65, 274-292.
P. Deheuvels (1981), A non parametric test for independence, Publ. Inst. Statist. Univ. Paris 26, 29-50.
K. Ghoudi, R. Kulperger, and B. Rémillard (2001), A nonparametric test of serial independence for times series and residuals, Journal of Multivariate Analysis, 79:191-218.
C. Genest and B. Rémillard (2004), Tests of independence and randomness based on the empirical copula process, Test 13, 335-369.
I. Kojadinovic and J. Yan (2008), Tests of multivariate serial independence based on a Möbius decomposition of the independence empirical copula process, submitted.
empcops.test,empcopu.test,empcopm.test,dependogram
## A multivariate time series d <- 2 n <- 100 param <- 0.25 ar <- matrix(0,2*n,d) ar[1,] <- rnorm(d) for (i in 2:(2*n)) ar[i,] <- matrix(param,d,d) %*% ar[i-1,] + rnorm(d) x <- ar[(n+1):(2*n),] ## Run the test test <- empcopsm.test(x,3) test ## Display the dependogram dependogram(test)