# spectrum

0th

Percentile

##### Spectral Density Estimation

The spectrum function estimates the spectral density of a time series.

Keywords
ts
##### 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 $2\pi$ 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 components:
• freqvector 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.
• specVector (for univariate series) or matrix (for multivariate series) of estimates of the spectral density at frequencies corresponding to freq.
• cohNULL 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 $i < j$.
• phaseNULL for univariate series. For multivariate time series a matrix containing the cross-spectrum phase between different series. The format is the same as coh.
• seriesThe name of the time series.
• snamesFor multivariate input, the names of the component series.
• methodThe 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.

##### 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.)

spec.ar, spec.pgram; plot.spec.
library(stats) 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")