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\footnotesize
\noindent Statistica Sinica {\bf 17}(2007), 635-666

\vspace{3pc} \normalsize
\centerline{\large\bf BAYESIAN DECISION THEORETIC SCALE-ADAPTIVE}
\vspace{2pt}
\centerline{\large\bf ESTIMATION OF A LOG-SPECTRAL DENSITY}
\vspace{.25cm}
\author{Marianna Pensky, Brani Vidakovic and Daniela De Canditiis}
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\centerline{\it University of Central Florida, Georgia Institute of Technology}
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\centerline{\it and I.A.C. CNR Italy}
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\begin{quotation}
\noindent {\it Abstract:}
The problem of estimating the log-spectrum of a stationary time series by Bayesian
shrinkage of empirical wavelet coefficients is studied. A model in the wavelet
domain that accounts for distributional properties of the log-periodogram at levels
of fine detail and approximate normality at coarse levels in the wavelet decomposition,
is proposed. The smoothing procedure, called BAMS-LP (Bayesian Adaptive Multiscale
Shrinker of Log-Periodogram), ensures that the reconstructed log-spectrum is sufficiently
noise-free. It is also shown that the resulting Bayes estimators are asymptotically
optimal (in the mean-squared error sense).

Comparisons with non-wavelet and wavelet-non-Bayesian methods are discussed. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Log-spectral density, spectral density, wavelets. \par
\end{quotation}
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