R: Spectral Density Estimation

spectrum {ts}

R Documentation

Spectral Density Estimation

Description

The spectrum function estimates the spectral density of a time series. This is a wrapper function which calls the methods spec.pgram and spec.ar.

The generic function plot has a method for spec objects: for multivariate time series it plots the marginal spectra of the series or pairs plots of the coherency and phase of the cross-spectra.

Usage

spectrum(x, method = c("pgram","ar"), plot = TRUE, ...)
plot.spec(spec.obj, add=FALSE, ci=0.95,
          log = c("yes", "dB", "no"), ci.col = "blue", ci.lty = 3, 
          plot.type = c("marginal", "coherency", "phase"), ...)

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".

plot

logical. If TRUE then the spectral density is plotted.

...

Further arguments to specific spec methods or plot.spec.

spec.obj

An object of class spec.

add

logical. If TRUE then lines are added to the existing plot.

ci

Coverage probability for confidence interval. Plotting of the confidence bar is omitted unless ci is strictly positive.

log

If "dB", plot on log10 (decibel) scale (as S-PLUS), otherwise use conventional log scale or linear scale. Logical values are also accepted. The default is "yes" unless options(ts.S.compat = TRUE) has been set, when it is "dB".

ci.col, ci.lty

Colour for plotting confidence bar, colour and line type for confidence intervals for coherency and phase.

plot.type

For multivariate time series, the type of plot required. Only the first character is needed.

...

Further graphical parameters.

Details

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 elements:

freq

vector of frequencies at which the spectral density is estimated. (Possibly approximate Fourier frequencies.)

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 spec objects 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. (1997) Modern Applied Statistics with S-PLUS. Second edition. Springer. (Especially pp. 437–442.)

Examples

## Examples from Venables & Ripley
## spec.pgram
par(mfrow=c(2,2))
data(lh)
spectrum(lh)
spectrum(lh, spans=3)
spectrum(lh, spans=c(3,3))
spectrum(lh, spans=c(3,5))

data(UKLungDeaths)
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")