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.
an (n,d)-dimensional matrix corresponding to a multivariate time series,
depending on the argument
the tapering method, either
should an asymptotic bias-correction under the affine-invariant Riemannian metric be applied to
the HPD periodogram matrix? Defaults to
a positive numeric value corresponding to the time-bandwidth parameter of the DPSS tapering functions,
method = "multitaper",
pdPgram calculates a (d,d)-dimensional multitaper
periodogram matrix based on B DPSS (Discrete Prolate Spheroidal Sequence or Slepian) orthogonal tapering functions
dpss applied to the d-dimensional time series
method = "bartlett",
pdPgram computes a Bartlett spectral estimator by averaging the periodogram matrices of
segments of the d-dimensional 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 affine-invariant 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 affine-invariant metric as explained in
\insertCiteCvS17pdSpecEst and Chapter 3 of \insertCiteC18pdSpecEst. The pre-smoothed HPD periodogram matrix
(i.e., an initial noisy HPD spectral estimator) can be given as input to the function
pdSpecEst1D to perform
intrinsic wavelet-based spectral matrix estimation. In this case, set
bias.corr = F (the default) as the appropriate
bias-corrections are applied internally by the function
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
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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