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Modeling of stationary periodic time series by ARMA representations
KTH. Shanghai Jiao Tong University, China.
2016 (English)In: Springer Optimization and Its Applications, Springer, 2016, 281-314 p.Conference paper, Published paper (Refereed)
Abstract [en]

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence (c0; c1;:::; cn) of covariance lags ck D E{y(t+k)y(t)} emanating from a stationary periodic process {y.(t)} with period 2N > 2n,find all possible rational spectral functions of {y.(t)} of degree at most 2n or,equivalently,all bilateral and unilateral ARMA models of order at most n,having this partial covariance sequence. Each representation is obtained as the solution of a pair of dual convex optimization problems. This theory is then reformulated in terms of circulant matrices and the connections to reciprocal processes and the covariance selection problem is explained. Next it is shown how the theory can be extended to the multivariate case. Finally,an application to image processing is presented.

Place, publisher, year, edition, pages
Springer, 2016. 281-314 p.
Keyword [en]
Bilateral ARMA models, Circulant covariance extension, Discrete moment problem, Image processing, Periodic processes
National Category
Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:kth:diva-202008DOI: 10.1007/978-3-319-42056-1_9Scopus ID: 2-s2.0-84992389385OAI: oai:DiVA.org:kth-202008DiVA: diva2:1077032
Note

QC 20170224

Available from: 2017-02-24 Created: 2017-02-24 Last updated: 2017-02-24Bibliographically approved

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