getCoherencySdNaive-SmoothedPG {quantspec}

Get estimates for the standard deviation of the coherency computed from smoothed quantile periodogram.

Description

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.

Usage

## S4 method for signature '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")
)

Arguments

object

SmoothedPG of which to get the estimates for the standard deviation.

frequencies

a vector of frequencies for which to get the result

levels.1

the first vector of levels for which to get the result

levels.2

the second vector of levels for which to get the result

d1

optional parameter that determine for which j1 to return the data; may be a vector of elements 1, ..., D

d2

same as d1, but for j2

type

can be "1", where cov(Z, Conj(Z)) is subtracted, or "2", where it's not

impl

choose "R" or "C" for one of the two implementations available

Details

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.

Value

Returns the estimate described above.

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]