# spectrum {stats}

Spectral Density Estimation
Package:
stats
Version:
R 3.0.2

### 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.

`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")```

### Author(s)

Martyn Plummer, B.D. Ripley

Documentation reproduced from R 3.0.2. License: GPL-2.