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spectrum: Spectral Density Estimation

spectrum

R Documentation

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`.

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.

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.

Author(s)

Martyn Plummer, B.D. Ripley

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.)

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")