Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods

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

Physica A: Statistical Mechanics and its Applications, 1997, vol. 246, issue 3, 609-632

Abstract: Precise reference signals are required to evaluate methods for characterizing a fractal time series. Here we use fGp (fractional Gaussian process) to generate exact fractional Gaussian noise (fGn) reference signals for one-dimensional time series. The average autocorrelation of multiple realizations of fGn converges to the theoretically expected autocorrelation. Two methods, commonly used to generate fractal time series, an approximate spectral synthesis (SSM) method and the successive random addition (SRA) method, do not give the correct correlation structures and should be abandoned. Time series from fGp were used to test how well several versions of rescaled range analysis (R/S) and dispersional analysis (Disp) estimate the Hurst coefficient (0 < H < 1.0). Disp is unbiased for H < 0.9 and series length N ⩾ 1024, but underestimates H when H > 0.9 R/S-detrended overestimates H for time series with H < 0.7 and underestimates H for H > 0.7. Estimates of H(Ĥ) from all versions of Disp usually have lower bias and variance than those from R/S. All versions of dispersional analysis, Disp, now tested on fGp, are better than we previously thought and are recommended for evaluating time series as long-memory processes.

Keywords: Fractals; Fractional Gaussian noise; Hurst coefficient; Exact simulation (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:246:y:1997:i:3:p:609-632

DOI: 10.1016/S0378-4371(97)00363-4

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