Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series

Michael J. Cannon, Donald B. Percival, David C. Caccia, Gary M. Raymond and James B. Bassingthwaighte

Physica A: Statistical Mechanics and its Applications, 1997, vol. 241, issue 3, 606-626

Abstract: Three-scaled windowed variance methods (standard, linear regression detrended, and bridge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed variance methods estimate H for fractional Brownian motion (fBm) signals which are cumulative sums of fractional Gaussian noise (fGn) signals. For all three methods both the bias and standard deviation of estimates are less than 0.05 for series having N ⩾ 29 points. Estimates for short series (N < 28) are unreliable. To have a 0.95 probability of distinguishing between two signals with true H differing by 0.1, more than 215 points are needed. All three methods proved more reliable (based on bias and variance of estimates) than Hurst's rescaled range analysis, periodogram analysis, and autocorrelation analysis, and as reliable as dispersional analysis. The latter methods can only be applied to fGn or differences of fBm, while the scaled windowed variance methods must be applied to fBm or cumulative sums of fGn.

Keywords: Fractals; Fractional Gaussian noise; Fractional Brownian motion; Autocorrelation; Covariance; Long memory processes; Dispersional analysis (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (24)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437197002525
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:241:y:1997:i:3:p:606-626

DOI: 10.1016/S0378-4371(97)00252-5

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().