# spectrum {stats}

### Description

The `spectrum`

function estimates the spectral density of a time series.

### 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"`

. - ...
- 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 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.

### Values

An object of class `"spec"`

, which is a list containing at least the following components:

The result is returned invisibly if `plot`

is true.

- 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.

### 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.)

### 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.

### See Also

`spec.ar`

, `spec.pgram`

; `plot.spec`

.

### Examples

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 R 3.0.2. License: GPL-2.