spectrum function estimates the spectral density of a time series.
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
- Further arguments to specific spec methods or
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.
An object of class
"spec", which is a list containing at least the following components:
The result is returned invisibly if
plot is true.
- 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 corresponding to
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.
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.)
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.
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")
Documentation reproduced from R 3.0.2. License: GPL-2.