ClippedFT-class {quantspec}

Class for Fourier transform of the clipped time series.

Description

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.

Details

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.

References

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]

See Also

For an example see FreqRep.