stats (version 3.3.3)

spectrum: Spectral Density Estimation

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". Can be abbreviated.

…

Further arguments to specific spec methods or plot.spec.

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.

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.

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

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")