TSA (version 1.3)

spec: Computing the spectrum

Description

This is a wrapper that allows the user to invoke either the spec.pgram function or the spec.ar function in the stats pacakge. Note that the seasonal attribute of the data, if it exists, will be removed, for our preferred way of presenting the output.

Usage

spec(x, taper = 0, detrend = FALSE, demean = TRUE, method = c("pgram", 
    "ar")[1], ci.plot = FALSE, ylim = range(c(lower.conf.band, upper.conf.band)), 
    ...)

Arguments

x

A univariate or multivariate time series

taper

amount of taper; 0 is the default

detrend

logical; if True, the data are detrended; default is False

demean

logical; if True, the data are centered; default is True

method

String specifying the method used to estimate the spectral density. Allowed methods are "pgram" (the default) and "ar".

ci.plot

logical; if True, the 95% confidence band will be plotted.

ylim

Plotting parameter vector specifying the minimum and maximum of the y-axis.

…

other arguments

Value

The output is from the spec.pgram function or spec.ar function, and the following description of the output is taken from the help manual of the spec function in the stats package. 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.

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 3927.)

Examples

# NOT RUN {
set.seed(271435); n=200; phi=-0.6
y=arima.sim(model=list(ar=phi),n=n)
k=kernel('daniell',m=15)
sp=spec(y,kernel=k,main='',sub='',xlab='Frequency',
ylab='Log(Smoothed Sample Spectrum)',ci.plot=TRUE,ci.col='black')
lines(sp$freq,ARMAspec(model=list(ar=phi),sp$freq,plot=FALSE)$spec,lty=4)
abline(h=0)
# }