Name of the wavelet filter to use in the decomposition. See
wave.filter for those wavelet filters available.
J
Depth of the discrete wavelet packet transform.
p
Level of significance for the white noise testing procedure.
dyadic
Logical parameter indicating whether or not the original
time series is dyadic in length.
frac
Fraction of the time series that should be used in
constructing the likelihood function.
Value
List containing the maximum likelihood estimates (MLEs) of
$\delta$, $f_G$ and $\sigma^2$, along with the value of
the likelihood for those estimates.
Details
The variance-covariance matrix of the original time series is
approximated by its wavelet-based equivalent. A Whittle-type
likelihood is then constructed where the sums of squared wavelet
coefficients are compared to bandpass filtered version of the true
spectral density function. Minimization occurs for the fractional
difference parameter $d$ and the Gegenbauer frequency $f_G$,
while the innovations variance is subsequently estimated.
References
Whitcher, B. (2003)
Wavelet-based estimation for seasonal long-memory processes.
Technical Report.