crossqreg.sb {quantilogram}

Stationary Bootstrap for the Cross-Quantilogram

Description

Returns critical values for the cross-quantilogram, based on the stationary bootstrap.

Usage

crossqreg.sb(DATA1, DATA2, vecA, k, gamma, Bsize, sigLev)

Arguments

DATA1

The original data matrix (T x p1)

DATA2

The original data matrix (T x p2)

vecA

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

k

A lag order

gamma

A parameter for the stationary bootstrap

Bsize

The number of repetition of bootstrap

sigLev

The statistical significance level

Details

This function generates critical values for for the cross-quantilogram, using the stationary bootstrap in Politis and Romano (1994).

Value

The boostrap 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. "The stationary bootstrap." Journal of the American Statistical Association 89.428 (1994): 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 10 for test 
sigLev = 0.05 ## significance level

## cross-quantilogram with the lag of 5, after quantile regression 
crossqreg.sb(D1, D2, vecA, 5, gamma, Bsize, sigLev)