The spectrum
function estimates the spectral density of a
time series.
1 
x 
A univariate or multivariate time series. 
method 
String specifying the method used to estimate the
spectral density. Allowed methods are 
... 
Further arguments to specific spec methods or

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.
An object of class "spec"
, which is a list containing at
least the following components:
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 
coh 

phase 

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 plot
is true.
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.
Martyn Plummer, B.D. Ripley
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 392–7.)
spec.ar
,
spec.pgram
;
plot.spec
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  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")

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