QRegEstimator is an S4 class that implements the necessary
calculations to determine the frequency representation based on the weigthed
\(L_1\)-projection of a time series as described in
Dette et. al (2015). As a subclass to FreqRep
it inherits slots and methods defined there.
methodmethod used for computing the quantile regression estimates.
The choice is passed to qr; see the
documentation of quantreg for details.
parallela flag that signalizes that parallelization mechanisms from the package snowfall may be used.
For each frequency \(\omega\) from frequencies and level
\(\tau\) from levels the statistic
$$\hat b^{\tau}_n(\omega) := \arg\max_{a \in R, b \in C}
\sum_{t=0}^{n-1}
\rho_{\tau}(Y_t - a - Re(b) \cos(\omega t) - Im(b) \sin(\omega t)),$$
is determined and stored to the array values.
The solution to the minimization problem is determined using the function
rq from the quantreg package.
All remarks made in the documentation of the super-class
FreqRep apply.
Dette, H., Hallin, M., Kley, T. & Volgushev, S. (2015). Of Copulas, Quantiles, Ranks and Spectra: an \(L_1\)-approach to spectral analysis. Bernoulli, 21(2), 781--831. [cf. http://arxiv.org/abs/1111.7205]