serialIndepTest {copula} | R Documentation |
Serial independence test based on the empirical copula process as
proposed in Ghoudi et al. (2001) and Genest and Rémillard (2004). The
test, which is the serial analog of indepTest
, can be
seen as composed of three steps: (i) a simulation step, which consists
in simulating the distribution of the test statistics under serial
independence for the sample size under consideration; (ii) the test
itself, which consists in computing the approximate p-values of the
test statistics with respect to the empirical distributions obtained
in step (i); and (iii) the display of a graphic, called a
dependogram, enabling to understand the type of departure from
serial independence, if any. More details can be found in the articles
cited in the reference section.
serialIndepTestSim(n, lag.max, m=lag.max+1, N=1000) serialIndepTest(x, d, alpha=0.05)
n |
Length of the time series when simulating the distribution of the test statistics under serial independence. |
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 repetitions when simulating under serial independence. |
x |
Numeric vector containing the time series whose serial independence is to be tested. |
d |
Object of class serialIndepTestDist as returned by the
function serialIndepTestSim . It can be regarded as the
empirical distribution of the test statistics under serial
independence. |
alpha |
Significance level used in the computation of the critical values for the test statistics. |
See the references below for more details, especially the third and fourth ones.
The function "serialIndepTestSim"
returns an object of class
"serialIndepTestDist"
whose attributes are: sample.size
,
lag.max
, max.card.subsets
, number.repetitons
,
subsets
(list of the subsets for which test statistics have
been computed), subsets.binary
(subsets in binary 'integer'
notation), dist.statistics.independence
(a N
line matrix
containing the values of the test statistics for each subset and each
repetition) and dist.global.statistic.independence
(a vector a
length N
containing the values of the serial version of the
global Cramér-von Mises test statistic for each repetition — see
last reference p.175).
The function "serialIndepTest"
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 serial independence
empirical copula process — see last reference p 175) and
global.statistic.pvalue
(corresponding p-value).
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.
C. Genest and B. Rémillard (2004), Tests of independence and randomness based on the empirical copula process. Test, 13:335–369.
C. Genest, J.-F. Quessy and B. Rémillard (2006). Local efficiency of a Cramer-von Mises test of independence, Journal of Multivariate Analysis, 97:274–294.
C. Genest, J.-F. Quessy and B. Rémillard (2007), Asymptotic local efficiency of Cramér-von Mises tests for multivariate independence. The Annals of Statistics, 35:166–191.
indepTest
,
multIndepTest
,
multSerialIndepTest
,
dependogram
## AR 1 process ar <- numeric(200) ar[1] <- rnorm(1) for (i in 2:200) ar[i] <- 0.5 * ar[i-1] + rnorm(1) x <- ar[101:200] ## In order to test for serial independence, the first step consists ## in simulating the distribution of the test statistics under ## serial independence for the same sample size, i.e. n=100. ## As we are going to consider lags up to 3, i.e., subsets of ## {1,...,4} whose cardinality is between 2 and 4 containing {1}, ## we set lag.max=3. This may take a while... d <- serialIndepTestSim(100,3) ## The next step consists in performing the test itself: test <- serialIndepTest(x,d) ## Let us see the results: test ## Display the dependogram: dependogram(test) ## NB: In order to save d for future use, the save function can be used.