Advances and Applications in Statistics
Volume 1, Issue 3, Pages 247 - 275
(December 2001)
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Algorithm of Local Information
Igor Zurbenko (U. S. A.)
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Abstract: Frequency analysis of a given process is needed when
we want to determine the major driving forces that
combine and generate the process. Information about
the composition of a process is usually sought in the
spectral density function. In this paper, our concern
is to build an optimal estimate for the spectral
density function that has a natural construction and
outperforms the existing methods of estimating the
spectra. We construct a non-parametric adaptive
spectral estimate that asymptotically minimizes the
cross-entropy between the estimate and the log of the
real spectral density function. The method has no
parametric limitations and is very successful for
estimating spectral density functions with varying
degrees of smoothness. Our algorithm (ALI) is based on
linearly approximating the local information present
in the process, which in turn leads to the smallest
information dissimilarity between our estimate and the
log of the true spectra. ALI is applied on a simulated
example and a comparison with other currently used
procedures is performed. |
Keywords and phrases: time series, spectral density, spectral estimations, periodogram, spectral window, KZ filtration, maximum entropy method, minimum cross-entropy. |
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