| QRegEstimator-class {quantspec} | R Documentation |
Class for quantile regression-based estimates in the harmonic linear model.
Description
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.
Details
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.
Slots
methodmethod used for computing the quantile regression estimates. The choice is passed to
qr; see the documentation ofquantregfor details.parallela flag that signalizes that parallelization mechanisms from the package snowfall may be used.
References
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]