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Fast and Exact Simulation of Complex-Valued Stationary Gaussian Processes Through Embedding Circulant Matrix

Lookup NU author(s): Professor Emilio Porcu

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Abstract

© 2018, © 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. This article is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly symmetric stationary Gaussian processes. We provide simple conditions on the complex covariance function ensuring the theoretical validity of the minimal embedding circulant matrix method. We show that these conditions are satisfied by many examples and illustrate the simulation algorithm. In particular, we present a simulation study involving the circularly symmetric fractional Gaussian noise, a model introduced in this article. Supplementary material for this article is available online.

Publication metadata

Author(s): Coeurjolly J-F, Porcu E

Publication type: Article

Publication status: Published

Journal: Journal of Computational and Graphical Statistics

Year: 2018

Volume: 27

Issue: 2

Pages: 278-290

Online publication date: 04/10/2017

Acceptance date: 02/04/2016

ISSN (print): 1061-8600

ISSN (electronic): 1537-2715

Publisher: American Statistical Association

URL: https://doi.org/10.1080/10618600.2017.1385468

DOI: 10.1080/10618600.2017.1385468

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