Moving Block Bootstrap for IVX-QR

Percentile confidence intervals and p-values for the IVX-QR coefficients from the moving block bootstrap (MBB) of Fan and Lee (2019, Section 5). Blocks of the pairs \((y_t, \tilde z_{t-1})\) are resampled and the quantile regression of Lee (2016) is refitted on each bootstrap sample. This avoids estimating the sparsity and the nuisance parameters that appear under conditional heteroskedasticity, which is where the asymptotic IVX-QR test is most distorted, especially in the tails.

Usage

ivx_qr_boot(object, B = 999, block = NULL, level = 0.95, seed = NULL)

# S3 method for class 'ivx_qr_boot'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

object

an object of class "ivx_qr".

B

number of bootstrap replications.

block

block length; the default is \(\lceil n^{1/4} \rceil\) as in the paper.

level

confidence level of the percentile intervals.

seed

optional integer seed.

x

an object of class "ivx_qr_boot".

digits

minimal number of significant digits.

...

unused.

Value

an object of class "ivx_qr_boot": a list with the estimates, the percentile intervals ci, two-sided percentile p-values p.value for \(H_0: \beta_j = 0\), and the bootstrap draws boot.

References

Fan, R., & Lee, J. H. (2019). Predictive quantile regressions under persistence and conditional heteroskedasticity. Journal of Econometrics, 213(1), 261-280.

Examples

if (requireNamespace("quantreg", quietly = TRUE)) {
  m <- ivx_qr(Ret ~ DP, data = kms, tau = 0.1)
  ivx_qr_boot(m, B = 199, seed = 1)
}
#> 
#> Call:
#> ivx_qr(formula = Ret ~ DP, data = kms, tau = 0.1)
#> 
#> IVX-QR at tau = 0.1, moving block bootstrap, B = 199, block length 6
#> 
#> Coefficients (percentile intervals and p-values):
#>     Estimate      2.5%     97.5% Pr(|b| > 0)
#> DP -0.024136 -0.057003  0.006266       0.131
#>