ClippedFT is an S4 class that implements the necessary
calculations to determine the Fourier transform of the clipped time
series. As a subclass to FreqRep it inherits
slots and methods defined there; it servers as a frequency representation of
a time series as described in Kley et. al (2016) for univariate time series
and in Barunik & Kley (2015) for multivariate time series.
For each frequency \(\omega\) from frequencies and level q
from levels the statistic
$$\sum_{t=0}^{n-1} I\{Y_{t,i} \leq q\} \mbox{e}^{-\mbox{i} \omega t}$$
is determined and stored to the array values. Internally the methods
mvfft and fft are used to achieve
good performance.
Note that, all remarks made in the documentation of the super-class
FreqRep apply.
Kley, T., Volgushev, S., Dette, H. & Hallin, M. (2016). Quantile Spectral Processes: Asymptotic Analysis and Inference. Bernoulli, 22(3), 1770--1807. [cf. http://arxiv.org/abs/1401.8104]
Barunik, J. & Kley, T. (2015). Quantile Cross-Spectral Measures of Dependence between Economic Variables. [preprint available from the authors]
For an example see FreqRep.