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 Probl. Peredachi Inf., 2008, Volume 44, Issue 1, Pages 45–58 (Mi ppi1265)

Methods of Signal Processing

Modified Sign Method for Testing the Fractality of Gaussian Noise

A. P. Kovalevskiiab

a Novosibirsk State Technical University
b Novosibirsk State University

Abstract: Fractal Gaussian noise is a stationary Gaussian sequence of zero-mean random variables whose sums possess the stochastic self-similarity property. If the random variables are independent, the self-similarity coefficient equals 1/2. The sign criterion for testing the hypothesis that the parameter equals 1/2 against the alternative $H\neq 1/2$ is based on counting the sign change rate for elements of the sequence. We propose a modification of the criterion: we count sign change indicators not only for the original random variables but also for random variables formed as sums of consecutive elements. The proof of the asymptotic normality of our statistics under the alternative hypothesis is based on the theorem on the asymptotics of the covariance of sign change indicators for a zero-mean stationary Gaussian sequence with a slowly decaying correlation function.

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English version:
Problems of Information Transmission, 2008, 44:1, 40–52

Bibliographic databases:

UDC: 621.391.1:519.237.5
Revised: 06.11.2007

Citation: A. P. Kovalevskii, “Modified Sign Method for Testing the Fractality of Gaussian Noise”, Probl. Peredachi Inf., 44:1 (2008), 45–58; Problems Inform. Transmission, 44:1 (2008), 40–52

Citation in format AMSBIB
\Bibitem{Kov08} \by A.~P.~Kovalevskii \paper Modified Sign Method for Testing the Fractality of Gaussian Noise \jour Probl. Peredachi Inf. \yr 2008 \vol 44 \issue 1 \pages 45--58 \mathnet{http://mi.mathnet.ru/ppi1265} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2416753} \zmath{https://zbmath.org/?q=an:1169.62071} \transl \jour Problems Inform. Transmission \yr 2008 \vol 44 \issue 1 \pages 40--52 \crossref{https://doi.org/10.1134/S0032946008010043} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255537100004} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44349092642} 

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This publication is cited in the following articles:
1. A. P. Kovalevskii, V. S. Kostin, V. E. Khitsenko, “Modelirovanie i identifikatsiya posledovatelnosti zavisimykh sluchainykh velichin s simmetrichnym ustoichivym raspredeleniem”, Sib. zhurn. industr. matem., 13:4 (2010), 25–37
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