mADCFplot {dCovTS}

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)

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.

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.

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.

Note

The function plots only the biased estimator of ADCF matrix.

Author(s)

Maria Pitsillou and Konstantinos Fokianos.

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

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