fts.spectral.density {freqdom.fda} | R Documentation |
Functional spectral and cross-spectral density operator
Description
Estimates the spectral density operator and cross spectral density operator of functional time series.
Usage
fts.spectral.density(
X,
Y = X,
freq = (-1000:1000/1000) * pi,
q = ceiling((dim(X$coefs)[2])^{ 0.33 }),
weights = "Bartlett"
)
Arguments
X |
an object of class |
Y |
an object of class |
freq |
a vector containing frequencies in |
q |
window size for the kernel estimator, i.e. a positive integer. By default we choose |
weights |
kernel used in the spectral smoothing. For possible choices see
|
Details
Let and
be two samples of functional data. The cross-spectral density kernel between the two time series
and
is defined as
The function fts.spectral.density
determines the empirical
cross-spectral density kernel between the two time series. The estimator is of the
form
with defined in
fts.cov.structure
.
The other paremeters are as in cov.structure
.
Since and
we can write
where is defined as for the function
spectral.density
for series of coefficient vectors
and
.
Value
Returns an object of class fts.timedom
. The list is containing the following components:
-
operators
an array. Element
[,,k]
in the coefficient matrix of the spectral density matrix evaluated at the-th frequency listed in
freq
. -
lags
returns the lags vector from the arguments.
-
basisX
returns
X$basis
, an object of classbasis.fd
(seecreate.basis
). -
basisY
returns
Y$basis
, an object of classbasis.fd
(seecreate.basis
)
See Also
The multivariate equivalent in the freqdom
package: spectral.density
Examples
data(pm10)
X = center.fd(pm10)
# Compute the spectral density operator with Bartlett weights
SD = fts.spectral.density(X, freq = (-50:50/50) * pi, q = 2, weight="Bartlett")
fts.plot.operators(SD, freq = -2:2)
# Compute the spectral density operator with Tukey weights
SD = fts.spectral.density(X, freq = (-50:50/50) * pi, q = 2, weight="Tukey")
fts.plot.operators(SD, freq = -2:2)
# Note relatively small difference between the two plots
# Now, compute the spectral density operator with Tukey weights and larger q
SD = fts.spectral.density(X, freq = (-50:50/50) * pi, q = 5, weight="Tukey")
fts.plot.operators(SD, freq = -2:2)