Synthesis of multivariate stationary series with prescribed marginal distributions and covariance using circulant matrix embeddi

The problem of synthesizing multivariate stationary series Y [n] = (Y1[n], . . . , YP [n])T , n ∈ Z, with prescribed non-Gaussian marginal distributions, and a targeted covariance structure, is addressed. The focus is on constructions based on a memoryless transformation Yp[n] = fp(Xp[n]) of a multivariate stationary Gaussian series X[n] = (X1[n], . . . , XP [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 fp for a prescribed marginal distribution are discussed in a comprehensive manner. The interplay between the targeted marginal distributions, the choice of the transforms fp, 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 sim...

• Type: Journal
• Year: 2011
• Where: SIGPRO
• Authors: Hannes Helgason, Vladas Pipiras, Patrice Abry
• Keywords: Covariance Structure, Database, Gaussian Series, Marginal Distributions, SIGPRO 2011