# 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 S-PLUS. This makes the spectral density a density over the
range `(-frequency(x)/2, +frequency(x)/2]`

, whereas a more common
scaling is $2\pi$ 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
`"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 `freq`

.coh `NULL`

for univariate series. For multivariate time series, a matrix containing the*squared*coherency between different series. Column $i + (j - 1) * (j - 2)/2$ of`coh`

contains the squared coherency between columns $i$ and $j$ of`x`

, where $i < j$.phase `NULL`

for univariate series. For multivariate time series a matrix containing the cross-spectrum phase between different series. The format is the same as`coh`

.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.

##### 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 S-PLUS.* Fourth edition. Springer. (Especially
pages 392--7.)

##### 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")
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*