SmoothedPG is an S4 class that implements the necessary
calculations to determine a smoothed version of one of the quantile
periodograms defined in Dette et. al (2015), Kley et. al (2016) and
Barunik&Kley (2015).
envAn environment to allow for slots which need to be accessable in a call-by-reference manner:
sdNaiveAn array used for storage of the naively estimated standard deviations of the smoothed periodogram.
sdNaive.freqa vector indicating for which frequencies
sdNaive has been computed so far.
sdNaive.donea flag indicating whether sdNaive
has been set yet.
sdBootAn array used for storage of the standard deviations of the smoothed periodogram, estimated via bootstrap.
sdBoot.donea flag indicating whether
sdBoot.naive has been set yet.
qPGthe QuantilePG to be smoothed
weightthe Weight to be used for smoothing
For a QuantilePG \(Q^{j_1, j_2}_n(\omega, x_1, x_2)\) and
a Weight \(W_n(\cdot)\) the smoothed version
$$\frac{2\pi}{n} \sum_{s=1}^{n-1} W_n(\omega-2\pi s / n) Q^{j_1, j_2}_n(2\pi s / n, x_1, x_2)$$
is determined.
The convolution required to determine the smoothed periodogram is implemented
using convolve.