Qstat.sb.opt {quantilogram}

Stationary Bootstrap for Q statistics

Description

Stationary Bootstrap procedure to generate critical values for both Box-Pierece and Ljung-Box type Q-statistics with the choice of the stationary-bootstrap parameter.

Usage

Qstat.sb.opt(DATA, vecA, Psize, Bsize, sigLev)

Arguments

DATA

The original data

vecA

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

Psize

The maximum number of lags

Bsize

The number of repetition of bootstrap

sigLev

The statistical significance level

Details

This function returns critical values for for both Box-Pierece and Ljung-Box type Q-statistics through the statioanry bootstrap proposed by 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.

Value

The bootstrap critical values

Author(s)

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

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

# 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

## Q statistics with lags from 1 to5
Qstat.sb.opt(D, vecA, 5, Bsize, sigLev)