Correlation properties of (discrete) fractional Gaussian noise and fractional Brownian motion
type: Item
instance of: scholarly article
title: Correlation properties of (discrete) fractional Gaussian noise and fractional Brownian motion
zbMATH Open document ID: 1393.60036
DOI: 10.1155/2015/485623
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm) has been widely used for modeling and interpreting physiological and behavioral data. The concept of \(1/f\) noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach. It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of ``ideal'' \(1/f\) noise. In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm). We especially derive a new analytical expression of the autocorrelation function (ACF) of dfBm. We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively. We show that, as \(H\) approaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line. Conversely, as \(H\) approaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise. These results reveal a severe breakdown of correlation properties around the \(1/f\) boundary and challenge the idea of a smooth transition between dfGn and dfBm processes. We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 6926462
Wikidata QID: Q59118711
author: D. Delignières
describes a project that uses: longmemo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/485623
OpenAlex ID: W1587780681
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description: scientific article; zbMATH DE number 6926462