multSerialIndepTest {copula}

Serial Independence Test for Multivariate Time Series via Empirical Copula

Description

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.

Usage

multSerialIndepTest(x, lag.max, m = lag.max+1, N = 1000, alpha = 0.05,
                    verbose = interactive())

Arguments

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 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.

verbose

a logical specifying if progress should be displayed via txtProgressBar.

Details

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.

Value

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).

References

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.

See Also

serialIndepTest, indepTest, multIndepTest, dependogram

Examples

## 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)