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)