Description Usage Arguments Details Value References See Also Examples
Given a multivariate time series, pdPgram
computes a multitapered HPD periodogram matrix based on
averaging raw Hermitian PSD periodogram matrices of tapered multivariate time series segments.
1 2 
X 
an (n,d)dimensional matrix corresponding to a multivariate time series,
with the 
B 
depending on the argument 
method 
the tapering method, either 
bias.corr 
should an asymptotic biascorrection under the affineinvariant Riemannian metric be applied to
the HPD periodogram matrix? Defaults to 
nw 
a positive numeric value corresponding to the timebandwidth parameter of the DPSS tapering functions,
see also 
If method = "multitaper"
, pdPgram
calculates a (d,d)dimensional multitaper
periodogram matrix based on B DPSS (Discrete Prolate Spheroidal Sequence or Slepian) orthogonal tapering functions
as in dpss
applied to the ddimensional time series X
. If method = "bartlett"
,
pdPgram
computes a Bartlett spectral estimator by averaging the periodogram matrices of B
nonoverlapping
segments of the ddimensional time series X
. Note that Bartlett's spectral estimator is a
specific (trivial) case of a multitaper spectral estimator with uniform orthogonal tapering windows.
In the case of subsequent periodogram matrix denoising in the space of HPD matrices equipped with the
affineinvariant Riemannian metric, one should set bias.corr = T
, thereby correcting for the asymptotic
bias of the periodogram matrix in the manifold of HPD matrices equipped with the affineinvariant metric as explained in
\insertCiteCvS17pdSpecEst and Chapter 3 of \insertCiteC18pdSpecEst. The presmoothed HPD periodogram matrix
(i.e., an initial noisy HPD spectral estimator) can be given as input to the function pdSpecEst1D
to perform
intrinsic waveletbased spectral matrix estimation. In this case, set bias.corr = F
(the default) as the appropriate
biascorrections are applied internally by the function pdSpecEst1D
.
A list containing two components:

vector of n/2 frequencies in the range [0,0.5) at which the periodogram is evaluated. 

a (d, d, n/2)dimensional array containing the
(d,d)dimensional multitaper periodogram matrices at frequencies corresponding
to 
1 2 3 4 5 6 7  ## ARMA(1,1) process: Example 11.4.1 in (Brockwell and Davis, 1991)
Phi < array(c(0.7, 0, 0, 0.6, rep(0, 4)), dim = c(2, 2, 2))
Theta < array(c(0.5, 0.7, 0.6, 0.8, rep(0, 4)), dim = c(2, 2, 2))
Sigma < matrix(c(1, 0.71, 0.71, 2), nrow = 2)
ts.sim < rARMA(200, 2, Phi, Theta, Sigma)
ts.plot(ts.sim$X) # plot generated time series traces
pgram < pdPgram(ts.sim$X)

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