quantilogram (version 3.1.1)

crossq.sb.opt: Stationary Bootstrap for the Cross-Quantilogram with the choice of the stationary-bootstrap parameter

Description

Returns critical values for the cross-quantilogram, based on the stationary bootstrap with the choice of the stationary-bootstrap parameter.

Usage

crossq.sb.opt(DATA, vecA, k, Bsize, sigLev = 0.05)

Value

The boostrap critical values

Arguments

DATA

An input matrix of dimensions T x 2, where T is the number of observations. Column 1 contains the first variable and Column 2 contains the second variable. This function will apply a k-period lag to the second variable during computation.

vecA

A pair of two probability values at which sample quantiles are estimated

k

A lag order

Bsize

The number of repetition of bootstrap

sigLev

The statistical significance level. Default is 0.05 (5% significance level).

Author

Heejoon Han, Oliver Linton, Tatsushi Oka and Yoon-Jae Whang

Details

This function generates critical values for for the cross-quantilogram, using the stationary bootstrap in Politis and Romano (1994). To choose parameter for the statioanry bootstrap, this function first obtaines the optimal value for each time serie using the result provided by Politis and White (2004) and Patton, Politis and White (2004) (The R-package, "np", written by Hayfield and Racine is used). Next, the average of the obtained values is used as the parameter value.

References

Han, H., Linton, O., Oka, T., and Whang, Y. J. (2016). "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series." Journal of Econometrics, 193(1), 251-270.

Patton, A., Politis, D. N., and White, H. (2009). Correction to "Automatic block-length selection for the dependent bootstrap" by D. Politis and H. White. Econometric Reviews, 28(4), 372-375.

Politis, D. N., and White, H. (2004). "Automatic block-length selection for the dependent bootstrap." Econometric Reviews, 23(1), 53-70.

Politis, Dimitris N., and Joseph P. Romano. (1994). "The stationary bootstrap." Journal of the American Statistical Association 89.428: 1303-1313.

Examples

## data source
data("sys.risk")

## data: 2 variables
D = sys.risk[,c("Market", "JPM")]

# probability levels for the 2 variables
vecA = c(0.1, 0.5)

## setup for stationary bootstrap
Bsize  = 5    ## small size 5 for test
sigLev = 0.05 ## significance level

## cross-quantilogram with the lag of 5
crossq.sb.opt(D, vecA, 5, Bsize, sigLev)