multSerialIndepTest | R Documentation |
Analog of the serial independence test based on the empirical
copula process proposed by Christian Genest and Bruno Rémillard (see
serialIndepTest
) for multivariate time
series. The main difference comes from the fact that critical values
and p-values are obtained through the bootstrap/permutation
methodology, since, here, test statistics are not distribution-free.
multSerialIndepTest(x, lag.max, m = lag.max+1, N = 1000, alpha = 0.05,
verbose = interactive())
x |
data frame or matrix of multivariate 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
|
N |
number of bootstrap/permutation samples. |
alpha |
significance level used in the computation of the critical values for the test statistics. |
verbose |
a logical specifying if progress
should be displayed via |
See the references below for more details, especially the last one.
The former argument print.every
is deprecated and not
supported anymore; use verbose
instead.
The function "multSerialIndepTest"
returns an object of class
"indepTest"
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).
Deheuvels, P. (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.
Deheuvels, P. (1981) A non parametric test for independence. Publ. Inst. Statist. Univ. Paris 26, 29–50.
Genest, C. and Rémillard, B. (2004) Tests of independence and randomness based on the empirical copula process. Test 13, 335–369.
Ghoudi, K., Kulperger, R., and Rémillard, B. (2001) A nonparametric test of serial independence for times series and residuals. Journal of Multivariate Analysis 79, 191–218.
Kojadinovic, I. and Yan, J. (2011) Tests of multivariate serial independence based on a Möbius decomposition of the independence empirical copula process. Annals of the Institute of Statistical Mathematics 63, 347–373.
serialIndepTest
,
indepTest
,
multIndepTest
,
dependogram
## A multivariate time series {minimal example for demo purposes}
d <- 2
n <- 100 # sample size *and* "burn-in" size
param <- 0.25
A <- matrix(param,d,d) # the bivariate AR(1)-matrix
set.seed(17)
ar <- matrix(rnorm(2*n * d), 2*n,d) # used as innovations
for (i in 2:(2*n))
ar[i,] <- A %*% ar[i-1,] + ar[i,]
## drop burn-in :
x <- ar[(n+1):(2*n),]
## Run the test
test <- multSerialIndepTest(x,3)
test
## Display the dependogram
dependogram(test,print=TRUE)
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