Block Bootstrap Methods for Quantile Regression in Time Series

Description

Implements moving-blocks bootstrap and extended tapered-blocks bootstrap, as well as smooth versions of each, for quantile regression in time series. This package accompanies the paper: Gregory, K. B., Lahiri, S. N., & Nordman, D. J. (2018). A smooth block bootstrap for quantile regression with time series. The Annals of Statistics, 46(3), 1138-1166.

Details

Implements moving-blocks bootstrap and extended tapered-blocks bootstrap, as well as smooth versions of each, for quantile regression in time series. This package accompanies Gregory et al. (2018).

Index of help topics:

QregBB                  Implements MBB, ETBB, SMBB, and SETBB for
                        quantile regression
QregBB-package          Block Bootstrap Methods for Quantile Regression
                        in Time Series
getNPPIblksizesQR       Chooses block sizes for MBB, ETBB, SMBB, and
                        SETBB via the NPPI for quantile regression

The main function is the QregBB function, which implements the moving-blocks bootstrap (MBB), the extended tapered-blocks bootstrap (ETBB), and smooth versions of each (SMBB, SETBB). The function getNPPIblksizesQR chooses the block size based on the non-parametric plug-in method described in Lahiri (2013). For the smooth methods, the bandwidth is chosen by using the function bw.SJ function on the fitted residuals; then the bandwidth matrix is the identity matrix times the value returned by bw.SJ.

Author(s)

Karl Gregory

Maintainer: Karl Gregory <gregorkb@stat.sc.edu>

References

Gregory, K. B., Lahiri, S. N., & Nordman, D. J. (2018). A smooth block bootstrap for quantile regression with time series. The Annals of Statistics, 46(3), 1138-1166.

Lahiri, S. N. (2013). Resampling methods for dependent data. Springer Science & Business Media.

Examples

n <- 100
X1 <- arima.sim(model=list(ar=c(.7,.1)),n)
X2 <- arima.sim(model=list(ar=c(.2,.1)),n)
e <- arima.sim(model=list(ar=c(.7,.1)),n)
Y <- X1 + e
X <- cbind(rep(1,n),X1,X2)

QregBB.out <- QregBB(Y,X,tau=.5,l=4,B=500,h=NULL,alpha=0.05)
QregBB.out

Implements MBB, ETBB, SMBB, and SETBB for quantile regression

Description

Implements MBB, ETBB, SMBB, and SETBB for quantile regression

Usage

QregBB(Y, X, tau, l, B = 500, h = NULL, alpha = 0.05)

Arguments

Value

A list is returned containing for the MBB, SMBB, ETBB, and SETBB the set of Monte Carlo draws of the pivot quantity \sqrt{n}(\hat \beta^*_n - \tilde \beta_n), confidence intervals for each component of \beta corresponding to the specified confidence level, and estimates of the asymptotic covariance matrix of the pivot quantity \sqrt{n}(\hat \beta_n - \beta).

References

#' @references

Gregory, K. B., Lahiri, S. N., & Nordman, D. J. (2018). A smooth block bootstrap for quantile regression with time series. *The Annals of Statistics*, 46(3), 1138-1166.

See Also

A 'print.QregBB' method exists which prints to the console the bootstrap standard errors for each coefficient estimator from the MBB, SMBB, ETBB, and SETBB methods as well as confidence intervals for each coefficient at the specified level.

Examples

# generate some data and perform block-bootstrap methods
n <- 100
X1 <- arima.sim(model=list(ar=c(.7,.1)),n)
X2 <- arima.sim(model=list(ar=c(.2,.1)),n)
e <- arima.sim(model=list(ar=c(.7,.1)),n)
Y <- X1 + e
X <- cbind(rep(1,n),X1,X2)

QregBB.out <- QregBB(Y,X,tau=.5,l=4,B=500,h=NULL,alpha=0.05)
QregBB.out

Chooses block sizes for MBB, ETBB, SMBB, and SETBB via the NPPI for quantile regression

Description

Chooses block sizes for MBB, ETBB, SMBB, and SETBB via the NPPI for quantile regression

Usage

getNPPIblksizesQR(Y, X, tau, min.in.JAB = 100)

Arguments

Details

This function is based on the nonparametric plug-in (NPPI) method discussed in Lahiri (2003), which makes use of the jackknife-after-bootstrap (JAB).

Value

Returns a list of the NPPI-selected block sizes for the MBB, SMBB, ETBB, and SETBB.

References

Gregory, K. B., Lahiri, S. N., & Nordman, D. J. (2018). A smooth block bootstrap for quantile regression with time series. The Annals of Statistics, 46(3), 1138-1166.

Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer, New York.

Examples

# generate some data and use NPPI to choose block sizes for MBB, SMBB, ETBB, and SETBB.
n <- 50
X1 <- arima.sim(model=list(ar=c(.7,.1)),n)
X2 <- arima.sim(model=list(ar=c(.2,.1)),n)
e <- arima.sim(model=list(ar=c(.7,.1)),n)
Y <- X1 + e
X <- cbind(rep(1,n),X1,X2)

blksize.out <- getNPPIblksizesQR(Y,X,tau=.5)
blksize.out