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On adaptive covariance and spectrum estimation of locally stationary multivariate processes

Abstrakt

When estimating the correlation/spectral structure of a locally stationary process, one has to make two important decisions. First, one should choose the so-called estimation bandwidth, inversely proportional to the effective width of the local analysis window, in the way that complies with the degree of signal nonstationarity. Too small bandwidth may result in an excessive estimation bias, while too large bandwidth may cause excessive estimation variance. Second, but equally important, one should choose the appropriate order of the spectral representation of the signal so as to correctly model its resonant structure – when the order is too small, the estimated spectrum may not reveal some important signal components (resonances), and when it is too high, it may indicate the presence of some nonexistent components. When the analyzed signal is not stationary, with a possibly time-varying degree of nonstationarity, both the bandwidth and order parameters should be adjusted in an adaptive fashion.Thepaperpresentsandcomparesthreeapproachesallowingforunifiedtreatmentoftheproblem of adaptive bandwidth and order selection for the purpose of identification of nonstationary vector autoregressive processes: the cross-validation approach, the full cross-validation approach, and the approach that incorporates the multivariate version of the generalized Akaike’s final prediction error criterion. It is shown that the latter solution yields the best results and, at the same time, is very attractive from the computational viewpoint.

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Accepted albo Published Version
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Creative Commons: CC-BY-NC-ND otwiera się w nowej karcie

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
AUTOMATICA nr 82, strony 1 - 12,
ISSN: 0005-1098
Język:
angielski
Rok wydania:
2017
Opis bibliograficzny:
Niedźwiecki M., Ciołek M., Kajikawa Y.: On adaptive covariance and spectrum estimation of locally stationary multivariate processes// AUTOMATICA. -Vol. 82, (2017), s.1-12
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1016/j.automatica.2017.04.033
Weryfikacja:
Politechnika Gdańska

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