Spec {ftsspec} | R Documentation |
Compute Spectral Density of Functional Time Series
Description
This function estimates the spectral density operator of a Functional Time Series (FTS)
Usage
Spec(X, W = Epanechnikov_kernel, B.T = (dim(X)[1])^(-1/5),
only.diag = FALSE, trace = FALSE, demean = TRUE, subgrid = FALSE,
subgrid.density = 10, verbose = 0,
subgrid.density.relative.to.bandwidth = TRUE)
Arguments
X |
A |
W |
The weight function used to smooth the periodogram operator. Set by default to be the Epanechnikov kernel |
B.T |
The bandwidth of frequencies over which the periodogram operator
is smoothed. If |
only.diag |
A logical variable to choose if the function only computes
the marginal spectral density of each basis coordinate
( |
trace |
A logical variable to choose if only the trace of the spectral
density operator is computed. |
demean |
A logical variable to choose if the FTS is centered before computing its spectral density operator. |
subgrid |
A logical variable to choose if the spectral density operator
is only returned for a subgrid of the Fourier frequencies, which can be
useful in large datasets to reduce memory usage. |
subgrid.density |
Only used if |
verbose |
A variable to show the progress of the computations. By
default, |
subgrid.density.relative.to.bandwidth |
logical parameter to specify if
|
Value
A list containing the following elements:
- spec
The estimated spectral density operator. The first dimension corresponds to the different frequencies over which the spectral density operators are estimated.
- omega
The frequencies over which the spectral density is estimated.
- m
The number of Fourier frequencies over which the periodogram operator was smoothed.
- bw
The equivalent Bandwidth used in the weight function W(), as defined in Bloomfield (1976, p.201).
- weight
The weight function used to smooth the periodogram operator.
- kappa.square
The L2 norm of the weight function W.
References
spec.pgram function of R.
Bloomfield, P. (1976) "Fourier Analysis of Time Series: An Introduction", Wiley.
Panaretos, V. M. and Tavakoli, S., "Fourier Analysis of Functional Time Series", Ann. Statist. Volume 41, Number 2 (2013), 568-603.
Examples
ma.scale1=c(-1.4,2.3,-2)
a1=Generate_filterMA(10, 10, MA.len=3, ma.scale=ma.scale1)
X=Simulate_new_MA(a1, T.len=512, noise.type='wiener')
ans=Spec(X, trace=FALSE, only.diag=FALSE)
plot(ans)
plot(Spec(X, trace=FALSE, only.diag=FALSE, subgrid=TRUE, subgrid.density=10,
subgrid.density.relative.to.bandwidth=FALSE))
rm(ans)