Spectral Density Estimation
spectrum function estimates the spectral density of a
spectrum(x, ..., method = c("pgram", "ar"))
- A univariate or multivariate time series.
- 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
The spectrum here is defined with scaling
following S-PLUS. This makes the spectral density a density over the
(-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.
An object of class
- 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.
- Vector (for univariate series) or matrix (for multivariate
series) of estimates of the spectral density at frequencies
NULLfor univariate series. For multivariate time series, a matrix containing the squared coherency between different series. Column $ i + (j - 1) * (j - 2)/2$ of
cohcontains the squared coherency between columns $i$ and $j$ of
x, where $i < j$.
NULLfor univariate series. For multivariate time series a matrix containing the cross-spectrum phase between different series. The format is the same as
- The name of the time series.
- For multivariate input, the names of the component series.
- The method used to calculate the spectrum. The result is returned invisibly if
"spec", which is a list containing at least the following components:
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.
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.)
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")