The R-S multitapers do not exhibit the remarkable
spectral-leakage suppression properties of the Thomson
prolate tapers, so that in spectra with large dynamic
range, power bleeds from the strong peaks into neighboring
frequency bands of low amplitude -- spectral leakage.
Prewhitening can ameliorate the problem, at least for red
spectra [see Chapter 9, Percival and Walden (1993)].The value of the AR.max argument is made absolute,
after which this function has essentially two modes of
operation (detailed below): [object Object],[object Object]
In the second case, the time series is filtered in the time
domain with a finite-impluse-response filter of
AR.max terms. The filter is found by solving the
Yule-Walker equations for which it is assumed the series
was generated by an autoregressive process, up to order
AR.max. Mean and trend (AR.max ==
0){
Power spectral density estimates can become badly biased
(especially at lower frequencies) if a signal of the form
$f(x) = A x + B$ is not removed from the series. If
detrend=TRUE a model of this form is removed over
the entire series using a linear least-squares estimator;
in this case a mean value is removed regardless of the
logical state of demean. To remove only a
mean value, set detrend=FALSE and (obviously)
demean=TRUE.
}
Auto Regressive (AR) innovations (AR.max
> 0){
When an autoregressive model is removed from a
non-stationary series, the residuals are known as
'innovations', and may be stationary (or very-nearly
stationary). This function fits an AR model [order at least
1, but up to and including AR(AR.max)] to the series
by solving the Yule-Walker equations; however, AIC is used
to estimate the highest significant order, which means that
higher-order components may not necessarily be fit. The
resulting innovations can be used to better estimate the
stationary component of the original signal, and possibly
in an interactive editing method.
Note that the method used here--solving the Yule-Walker
equations--is not a true maximum likelihood estimator;
hence the AIC is calculated based on the variance estimate
(no determinant). From ?ar: In ar.yw
the variance matrix of the innovations is computed from the
fitted coefficients and the autocovariance of x.
A quick way to determine whether this may be needed for the
series is to run acf on the series, and see if
significant non-zero lag correlations are found. A warning
is produced if the fit returns an AR(0) fit, indicating
that AR prewhitening most likely inappropriate for the
series, which is apparently stationary (or very nearly so).
(The innovations could end up having higher variance
than the input series in such a case.)
Note that AR.max is restricted to the range
$[1,N-1]$ where $N$ is the series length.
}