dCovTS (version 1.1)

mADCFplot: Distance cross-correlation plot

Description

The function computes and plots the estimator of the auto-distance correlation matrix mADCF.

Usage

mADCFplot(x, MaxLag = 15, ylim = NULL, b = 499, bootMethod = c("Wild Bootstrap",
          "Independent Bootstrap"))

Arguments

x

multivariate time series.

MaxLag

maximum lag order at which to plot mADCF. Default is 15.

ylim

numeric vector of length 2 indicating the y limits of the plot. The default value, NULL, indicates that the range \((0,v)\), where \(v\) is the maximum number between 1 and the empirical critical values, should be used.

b

the number of bootstrap replications for constructing the 95% empirical critical values. Default is 499.

bootMethod

character string indicating the method to use for obtaining the 95% critical values. Possible choices are "Wild Bootstrap" (the default) and "Independent Bootstrap"

Value

A plot of the estimated mADCF matrices. The function also returns a list with

matrices

Sample distance correlation matrices starting from lag 0.

bootMethod

The method followed for computing the 95% confidence intervals of the plot.

critical.value

The critical value shown in the plot.

Details

The 95% confidence intervals shown in the plot (dotted blue horizontal line) are computed simultaneously based on the independent wild bootstrap approach (Dehling and Mikosch, 1994; Shao, 2010; Leucht and Neumann, 2013), since the elements of mADCV (and thus mADCF) can be expressed as degenerate V-statistics of order 2. More details can be found in Fokianos and Pitsillou (2016).

In addition, mADCFplot provides the option of independent bootstrap to compute the simultaneous 95% critical values.

References

Dehling, H. and T. Mikosch (1994). Random quadratic forms and the bootstrap for U-statistics. Journal of Multivariate Analysis \(\textbf{51}\), 392-413, http://dx.doi.org/10.1006/jmva.1994.1069

Fokianos K. and M. Pitsillou (2016). Testing pairwise independence for multivariate time series by the auto-distance correlation matrix. Submitted for publication.

Leucht, A. and M. H. Neumann (2013). Dependent wild bootstrap for degenerate U- and V- statistics. Journal of Multivariate Analysis \(\textbf{117}\), 257-280, http://dx.doi.org/10.1016/j.jmva.2013.03.003.

Shao, X. (2010). The dependent wild bootstrap. Journal of the American Statistical Association \(\textbf{105}\), 218-235, http://dx.doi.org/10.1198/jasa.2009.tm08744.

See Also

mADCF, mADCV

Examples

# NOT RUN {
x <- MASS::mvrnorm(100,rep(0,3),diag(3))
# }
# NOT RUN {
mADCFplot(x,18,ylim=c(0,0.5))
# }
# NOT RUN {
y <- MASS::mvrnorm(100,rep(0,6),diag(6))
# }
# NOT RUN {
mADCFplot(y,b=100)
# }
# NOT RUN {
deaths <- cbind(mdeaths,fdeaths)
# }
# NOT RUN {
mADCFplot(deaths,bootMethod="Indep")
# }