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Synthesis of multivariate stationary series with prescribed marginal distributions and covariance using circulant matrix embedding
KTH, School of Electrical Engineering (EES), Sound and Image Processing.
2011 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 91, no 8, 1741-1758 p.Article in journal (Refereed) Published
Abstract [en]

The problem of synthesizing multivariate stationary series Y[n] = (Y-1[n],...,Y-p[n](T), n is an element of Z, with prescribed non-Gaussian marginal distributions, and a targeted covariance structure, is addressed. The focus is on constructions based on a memoryless transformation Y-p[n] = f(p)(X-p[n]) of a multivariate stationary Gaussian series X[n] = (X-1[n],...,X-p[n])(T). The mapping between the targeted covariance and that of the Gaussian series is expressed via Hermite expansions. The various choices of the transforms f(p) for a prescribed marginal distribution are discussed in a comprehensive manner. The interplay between the targeted marginal distributions, the choice of the transforms f(p), and on the resulting reachability of the targeted covariance, is discussed theoretically and illustrated on examples. Also, an original practical procedure warranting positive definiteness for the transformed covariance at the price of approximating the targeted covariance is proposed, based on a simple and natural modification of the popular circulant matrix embedding technique. The applications of the proposed methodology are also discussed in the context of network traffic modeling. MATIAB codes implementing the proposed synthesis procedure are publicly available at

Place, publisher, year, edition, pages
2011. Vol. 91, no 8, 1741-1758 p.
Keyword [en]
Numerical synthesis, Multivariate Gaussian and non-Gaussian series, Circulant matrix embedding, Stationarity
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-35110DOI: 10.1016/j.sigpro.2011.01.020ISI: 000291291700006ScopusID: 2-s2.0-79955476890OAI: diva2:428604
QC 20110630Available from: 2011-06-30 Created: 2011-06-20 Last updated: 2011-09-07Bibliographically approved

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Helgason, Hannes
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