spp.mle.RdParameter estimation for a seasonal persistent (seasonal long-memory) process is performed via maximum likelihood on the wavelet coefficients.
spp.mle(y, wf, J=log(length(y),2)-1, p=0.01, frac=1)
spp2.mle(y, wf, J=log(length(y),2)-1, p=0.01, dyadic=TRUE, frac=1)| y | Not necessarily dyadic length time series. |
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| wf | Name of the wavelet filter to use in the decomposition. See
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| 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. |
List containing the maximum likelihood estimates (MLEs) of \(\delta\), \(f_G\) and \(\sigma^2\), along with the value of the likelihood for those estimates.
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.
Whitcher, B. (2004) Wavelet-based estimation for seasonal long-memory processes, Technometrics, 46, No. 2, 225-238.
B. Whitcher