Modeling of Stationary Periodic Time Series by ARMA Representations

Anders Lindquist () and Giorgio Picci ()
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Anders Lindquist: Shanghai Jiao Tong University
Giorgio Picci: University of Padova

A chapter in Optimization and Its Applications in Control and Data Sciences, 2016, pp 281-314 from Springer

Abstract: Abstract This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence (c 0, c 1, …, c n ) of covariance lags c k = 𝔼 { y ( t + k ) y ( t ) ¯ } $$c_{k} = \mathbb{E}\{y(t + k)\overline{y(t)}\}$$ 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.

Keywords: Discrete moment problem; Periodic processes; Circulant covariance extension; Bilateral ARMA models; Image processing (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-42056-1_9

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DOI: 10.1007/978-3-319-42056-1_9

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