QRegEstimator-class: Class for quantile regression-based estimates in the harmonic...

In quantspec: Quantile-Based Spectral Analysis of Time Series

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

method

method used for computing the quantile regression estimates. The choice is passed to qr; see the documentation of quantreg for details.

parallel

a 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]

quantspec documentation built on Sept. 11, 2024, 9:15 p.m.