Determines and returns an array of dimension [J,K1,K2],
where J=length(frequencies), K1=length(levels.1), and
K2=length(levels.2)). Whether
available or not, boostrap repetitions are ignored by this procedure.
At position (j,k1,k2)
the returned value is the standard deviation estimated corresponding to
frequencies[j], levels.1[k1] and levels.2[k2] that are
closest to the
frequencies, levels.1 and levels.2
available in object; closest.pos is used to determine
what closest to means.
# S4 method for SmoothedPG
getCoherencySdNaive(
object,
frequencies = 2 * pi * (0:(lenTS(object@qPG@freqRep@Y) -
1))/lenTS(object@qPG@freqRep@Y),
levels.1 = getLevels(object, 1),
levels.2 = getLevels(object, 2),
d1 = 1:(dim(object@values)[2]),
d2 = 1:(dim(object@values)[4]),
type = c("1", "2"),
impl = c("R", "C")
)Returns the estimate described above.
SmoothedPG of which to get the estimates for the
standard deviation.
a vector of frequencies for which to get the result
the first vector of levels for which to get the result
the second vector of levels for which to get the result
optional parameter that determine for which j1 to return the data; may be a vector of elements 1, ..., D
same as d1, but for j2
can be "1", where cov(Z, Conj(Z)) is subtracted, or "2", where it's not
choose "R" or "C" for one of the two implementations available
If not only one, but multiple time series are under study, the dimension of
the returned vector is of dimension [J,P,K1,P,K2], where P
denotes the dimension of the time series.
Requires that the SmoothedPG is available at all Fourier
frequencies from \((0,\pi]\). If this is not the case the missing
values are imputed by taking one that is available and has a frequency
that is closest to the missing Fourier frequency; closest.pos is used
to determine which one this is.
A precise definition on how the standard deviations of the smoothed quantile periodogram are estimated is given in Barunik and Kley (2015). The estimate returned is denoted by \(\sigma(\tau_1, \tau_2; \omega)\) on p. 26 of the arXiv preprint.
Note the ``standard deviation'' estimated here is not the square root of the complex-valued variance. It's real part is the square root of the variance of the real part of the estimator and the imaginary part is the square root of the imaginary part of the variance of the estimator.
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]