dCovTS (version 1.4)

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, alpha = 0.05, b = 499,
          bootMethod = c("Wild Bootstrap", "Independent Bootstrap"),
          ylim = NULL)

Value

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

matrices

Sample distance correlation matrices starting from lag 0.

bootMethod

The method followed for computing the \((1-\alpha)\)% confidence intervals of the plot.

critical.value

The critical value shown in the plot.

Arguments

x

A multivariate time series.

MaxLag

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

alpha

The significance level used to construct the \((1-\alpha)\)% empirical critical values.

b

The number of bootstrap replications for constructing the \((1-\alpha)\)% empirical critical values. Default is 499.

bootMethod

A character string indicating the method to use for obtaining the \((1-\alpha)\)% critical values. Possible choices are "Wild Bootstrap" (the default) and "Independent Bootstrap".

ylim

A 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.

Author

Maria Pitsillou and Konstantinos Fokianos.

Details

The \((1-\alpha)\)% 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 (2017).

In addition, mADCFplot provides the option of independent bootstrap to compute the simultaneous \((1-\alpha)\)% critical values.

References

Edelmann, D, K. Fokianos. and M. Pitsillou. (2019). An Updated Literature Review of Distance Correlation and Its Applications to Time Series. International Statistical Review, 87, 237-262.

Dehling, H. and T. Mikosch (1994). Random quadratic forms and the bootstrap for U-statistics. Journal of Multivariate Analysis, 51, 392-413.

Fokianos K. and Pitsillou M. (2018). Testing independence for multivariate time series via the auto-distance correlation matrix. Biometrika, 105, 337-352.

Fokianos K. and M. Pitsillou (2017). Consistent testing for pairwise dependence in time series. Technometrics, 159, 262-3270.

Huo, X. and G. J. Szekely. (2016). Fast Computing for Distance Covariance. Technometrics, 58, 435-447.

Leucht, A. and M. H. Neumann (2013). Dependent wild bootstrap for degenerate U- and V- statistics. Journal of Multivariate Analysis, 117, 257-280.

Pitsillou M. and Fokianos K. (2016). dCovTS: Distance Covariance/Correlation for Time Series. R Journal, 8, 324-340.

Shao, X. (2010). The dependent wild bootstrap. Journal of the American Statistical Association, 105, 218-235.

See Also

mADCF, mADCV

Examples

# \donttest{
### x <- matrix( rnorm(200), ncol = 2 )
### mADCFplot(x, 12, ylim = c(0, 0.5) )
### mADCFplot(x, 12, b = 100)
# }