spectrum
Spectral Density Estimation
The spectrum
function estimates the spectral density of a
time series.
 Keywords
 ts
Usage
spectrum(x, ..., method = c("pgram", "ar"))
Arguments
 x
 A univariate or multivariate time series.
 method
 String specifying the method used to estimate the
spectral density. Allowed methods are
"pgram"
(the default) and"ar"
. Can be abbreviated.  ...
 Further arguments to specific spec methods or
plot.spec
.
Details
spectrum
is a wrapper function which calls the methods
spec.pgram
and spec.ar
.
The spectrum here is defined with scaling 1/frequency(x)
,
following SPLUS. This makes the spectral density a density over the
range (frequency(x)/2, +frequency(x)/2]
, whereas a more common
scaling is $2pi$ and range $(0.5, 0.5]$ (e.g., Bloomfield)
or 1 and range $(pi, pi]$.
If available, a confidence interval will be plotted by
plot.spec
: this is asymmetric, and the width of the centre
mark indicates the equivalent bandwidth.
Value

An object of class
 freq
 vector of frequencies at which the spectral density is estimated. (Possibly approximate Fourier frequencies.) The units are the reciprocal of cycles per unit time (and not per observation spacing): see ‘Details’ below.
 spec
 Vector (for univariate series) or matrix (for multivariate
series) of estimates of the spectral density at frequencies
corresponding to
freq
.  coh
NULL
for univariate series. For multivariate time series, a matrix containing the squared coherency between different series. Column $ i + (j  1) * (j  2)/2$ ofcoh
contains the squared coherency between columns $i$ and $j$ ofx
, where $i < j$. phase
NULL
for univariate series. For multivariate time series a matrix containing the crossspectrum phase between different series. The format is the same ascoh
. series
 The name of the time series.
 snames
 For multivariate input, the names of the component series.
 method
 The method used to calculate the spectrum. The result is returned invisibly if
"spec"
, which is a list containing at
least the following components:
plot
is true.
Note
The default plot for objects of class "spec"
is quite complex,
including an error bar and default title, subtitle and axis
labels. The defaults can all be overridden by supplying the
appropriate graphical parameters.
References
Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.
Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. Second edition. Springer.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with SPLUS. Fourth edition. Springer. (Especially pages 3927.)
See Also
Examples
library(stats)
require(graphics)
## Examples from Venables & Ripley
## spec.pgram
par(mfrow = c(2,2))
spectrum(lh)
spectrum(lh, spans = 3)
spectrum(lh, spans = c(3,3))
spectrum(lh, spans = c(3,5))
spectrum(ldeaths)
spectrum(ldeaths, spans = c(3,3))
spectrum(ldeaths, spans = c(3,5))
spectrum(ldeaths, spans = c(5,7))
spectrum(ldeaths, spans = c(5,7), log = "dB", ci = 0.8)
# for multivariate examples see the help for spec.pgram
## spec.ar
spectrum(lh, method = "ar")
spectrum(ldeaths, method = "ar")