astsa (version 2.0)

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 and this can be used to replace spec.pgram.

Usage

mvspec(x, spans = NULL, kernel = NULL, taper = 0, pad = 0, 
         fast = TRUE, demean = FALSE, detrend = TRUE, 
         plot = TRUE, log='n', type = NULL, na.action = na.fail,
         nxm=2, nym=1, main=NULL, ...)

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.

details

matrix with columns: frequency, period, spectral ordinate(s)

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.

n.used

Sample length used for the FFT

df

Degrees of freedom (may be approximate) associated with the spectral estimate.

bandwidth

Bandwidth (may be approximate) associated with the spectral estimate.

method

The method used to calculate the spectrum.

The results are returned invisibly if plot is true.

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

log

same as spec.pgram but default is 'no'

type

type of plot to be drawn, defaults to lines

na.action

same as spec.pgram

nxm, nym

the number of minor tick mark divisions on x-axis, y-axis; the default is one minor tick on the x-axis and none on the y-axis

main

title of the graphics; if NULL, a suitable title is generated

...

graphical arguments passed to plot.spec

Details

This is built off of spec.pgram from the stats package with a few changes in the defaults and written so you can easily extract the estimate of the multivariate spectral matrix as fxx. The default for the plot is NOT to plot on a log scale and the graphic will have a grid. The bandwidth calculation has been changed to the more practical definition given in the text, \((L_h/n.used)*frequency(x)\). Also, the bandwidth is no longer displayed in the graphic. Although meant to be used to easily obtain multivariate spectral estimates, this script can be used for univariate time series. Note that the script does not taper by default (taper=0); this forces the user to do "conscious tapering".

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# real raw periodogram
mvspec(soi)
mvspec(soi, log='y')  # on a log scale

# smooth and some details printed
mvspec(soi, spans=c(7,7), taper=.5)$details[1:45,]

# multivariate example
deth = cbind(mdeaths, fdeaths)    # two R data sets, male/female monthly deaths ...
tsplot(deth, type='b', col=c(4,6), spaghetti=TRUE, pch=c('M','F'))
dog = mvspec(deth, spans=c(3,3), taper=.1)
dog$fxx        # look a spectral matrix estimates
dog$bandwidth  # bandwidth with time unit = year
dog$df         # degrees of freedom
plot(dog, plot.type="coherency")  # plot of squared coherency