Advances and Applications in Statistics
Volume 4, Issue 1, Pages 65 - 95
(April 2004)
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POWER CONTRIBUTION ANALYSIS FOR MULTIVARIATE TIME SERIES WITH CORRELATED NOISE SOURCES
Yoko Tanokura (Japan) and Genshiro Kitagawa (Japan)
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Abstract: Akaike’s
power contribution has been a useful concept
in detecting influential noise sources of
multivariate dynamic systems with feedback.
However, it is not applicable to systems with
significant correlations of noise, as it
requires the assumption that the variance
covariance matrix of the innovations is of
diagonal form. To address this problem, we
present a decomposition of the variance
covariance matrix, by modeling correlations
between two variables. Then, the general form
of the power spectrum is obtained and a new
power contribution that extends Akaike’s
concept is defined. It was shown that the
extended power contribution succeeds in
detecting the mutual influences among
cross-correlated noises of variables, and that
Akaike’s original power contribution
precisely captures some part of them. By
applying this method to three real data sets,
the known information was confirmed and new
information on cross-correlated noises was
explicitly detected. This extension has
significantly widened the applicable area of
this approach. |
Keywords and phrases: detection of noise source, Akaike’s power contribution, multivariate AR modeling, power spectrum, feedback system. |
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