astsa (version 1.1)

mvspec: Univariate and Multivariate Spectral Estimation

Description

This is spec.pgram with a few changes in the defaults and written so you can easily extract the estimate of the multivariate spectral matrix as fxx. The bandwidth calculation has been changed to the more practical definition given in the text. Can be used to replace spec.pgram for univariate series.

Usage

mvspec(x, spans = NULL, kernel = NULL, taper = 0, pad = 0, 
         fast = TRUE, demean = FALSE, detrend = TRUE, 
         plot = TRUE, na.action = na.fail, ...)

Arguments

x

univariate or multivariate time series (i.e., the p columns of x are time series)

spans

specify smoothing; same as spec.pgram

kernel

specify kernel; same as spec.pgram

taper

specify taper; same as spec.pgram with different default

pad

specify padding; same as spec.pgram

fast

specify use of FFT; same as spec.pgram

demean

if TRUE, series is demeaned first; same as spec.pgram

detrend

if TRUE, series is detrended first; same as spec.pgram

plot

plot the estimate; same as spec.pgram

na.action

same as spec.pgram

...

additional arguments; same as spec.pgram

Value

• An object of class "spec", which is a list containing at least the following components:
• fxx
  spectral matrix estimates; an array of dimensions dim = c(p,p,nfreq)
• freq
  vector of frequencies at which the spectral density is estimated.
• 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.
• Lh
  Number of frequencies (approximate) used in the band, as defined in (4.57) on page 204.
• n.used
  Sample length used for the FFT
• 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 results are returned invisibly if plot is true.

Details

This is spec.pgram with a few changes in the defaults and written so you can easily extract the estimate of the multivariate spectral matrix as fxx. The bandwidth calculation has been changed to the more practical definition given in the text, $(L_h/n.used)*frequency(x)$. Although meant to be used to easily obtain multivariate spectral estimates, this script can be used in Chapter 4 for the spectral analysis of a univariate time series. Note that the script does not taper by default (taper=0); this forces the user to do "conscious tapering". See Example 7.12 on page 461 for a demonstration.

References

http://www.stat.pitt.edu/stoffer/tsa3/

Examples

# univariate example
plot(co2)   # co2 is an R data set
mvspec(co2, spans=c(5,5), taper=.5)

# multivariate example
ts.plot(mdeaths, fdeaths, col=1:2)   # an R data set, male/female monthly deaths ...
dog = mvspec(cbind(mdeaths,fdeaths), spans=c(3,3), taper=.1)
dog$fxx        # look a spectral matrix estimates
dog$bandwidth  # bandwidth with time unit = year
dog$bandwidth/frequency(mdeaths)  # ... with time unit = month
plot(dog, plot.type="coherency")  # plot of squared coherency