Qstat.reg.sb {quantilogram}

Stationary Bootstrap for Q statistics

Description

Stationary Bootstrap procedure to generate critical values for both Box-Pierece and Ljung-Box type Q-statistics

Usage

Qstat.reg.sb(DATA1, DATA2, vecA, Psize, gamma, Bsize, sigLev)

Arguments

DATA1

The original data set (1)

DATA2

The original data set (2)

vecA

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

Psize

The maximum number of lags

gamma

A parameter for the stationary bootstrap

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).

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.

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

Examples

data(sys.risk) 

## sample size
T = nrow(sys.risk)

## matrix for quantile regressions
## - 1st column: dependent variables
## - the rest:   regressors or predictors 
D1 = cbind(sys.risk[2:T,"Market"], sys.risk[1:(T-1),"Market"])
D2 = cbind(sys.risk[2:T,"JPM"], sys.risk[1:(T-1),"JPM"])

## probability levels
vecA = c(0.1, 0.2)

## setup for stationary bootstrap
gamma  = 1/10 ## bootstrap parameter depending on data
Bsize  = 5    ## small size, 5, for test 
sigLev = 0.05 ## significance level

## Q statistics with lags from 1 to 5, after quantile regression 
Qstat.reg.sb(D1, D2, vecA, 5, gamma, Bsize, sigLev)