copula (version 0.999-19)

multSerialIndepTest: 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 R<U+00E9>millard (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.

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 <U+00E0> la Fisher of the subset statistic p-values), tippett.pvalue (a p-value resulting from a combination <U+00E0> 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 Cram<U+00E9>r-von Mises statistic derived directly from the independence empirical copula process - see In in the last reference) and global.statistic.pvalue (corresponding p-value).

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.

References

Deheuvels, P. (1979) La fonction de d<U+00E9>pendance empirique et ses propri<U+00E9>t<U+00E9>s: un test non param<U+00E9>trique d'ind<U+00E9>pendance. 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 R<U+00E9>millard, B. (2004) Tests of independence and randomness based on the empirical copula process. Test 13, 335--369.

Ghoudi, K., Kulperger, R., and R<U+00E9>millard, 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 M<U+00F6>bius decomposition of the independence empirical copula process. Annals of the Institute of Statistical Mathematics 63, 347--373.

See Also

serialIndepTest, indepTest, multIndepTest, dependogram

Examples

# NOT RUN {
## 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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