a list like the one returned by the function
ar.
It must have the components
ar,
var.pred and
order.
Component
ar is an
order by "nser" by "nser" array
of autoregressive coefficients
where
order is the autoregressive order and "nser" is
the number of components of the original multivariate series.
Component
var.pred is the prediction variance
(the innovations variance) of the series.
OPTIONAL ARGUMENTS:
n.freq
the number of frequencies between
0 and the Nyquist frequency
(=
frequency/2 cycles per unit time)
at which to compute the spectrum.
The default value is
n.used/2+1, where
n.used is the number of observations
not missing in the original time series.
This must be supplied if
n.used is not a component of
ar.list.
frequency
the sampling frequency for the time series.
The default is the frequency of the
resid component of
ar.list if
present, and
1 otherwise.
plot
if
TRUE, a plot of the spectrum will be produced.
VALUE:
a list containing the following components:
freq
the vector of frequencies between
0 and the Nyquist at which the spectrum
estimate is computed.
spec
a vector if a univariate series, and otherwise a matrix with columns
representing univariate series and rows corresponding
to the frequencies in
freq.
The spectrum estimate is in decibels (10 times log to base 10 transformation).
coh
a matrix containing the squared coherencies between each pair of series.
If j is less than k, then the pair (j,k) corresponds to column
(k-1)(k-2)/2 + j.
For univariate series this component is
NULL.
phase
a matrix like
coh containing the phase differences between
each pair of series (only for multivariate time series).
The units are radians.
These are made continuous by requiring that the first differences
be less than pi.
To put them back into the range [0, 2 pi) use the modulus operator
%%:
e.g.
reducedphase <- phase%%(2*pi).
For univariate series this component is
NULL.
order
the order of the autoregression in
ar.list.
method
a string describing the method used.
series
a string containing the name of the time series, if available from
ar.list.
SIDE EFFECTS:
If
plot=TRUE, a plot of the spectrum is produced.
SEE ALSO:
,
,
,
.
EXAMPLES:
ll.ar <- ar(log(lynx)) # Fit an AR model to the log of the lynx data
spec <- spec.pgram(log(lynx)) # and superimpose the raw periodogram for this
ll.spec.ar <- spec.ar(ll.ar, plot=F) # data and its autoregressive spectrum.
spec.plot(ll.spec.ar, add=T)