2003/03/21 by A. Carbone, Anna Carbone, Carbone, Anna +3
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #FOS: Physical sciences #Image and Signal Denoising Methods #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0303465
9 pages, 4 figures, submitted to Physical Review E
arxiv created 2003/03/21 · openalex publication_date 2003/03/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hurst coefficient H of a stochastic fractal signal is estimated using the function σMA2=\frac1Nmax-n∑i=n^Nmax [y(i)-\widetildeyn(i)]2, where \widetildeyn(i) is defined as 1/n ∑k=0n-1 y(i-k), n is the dimension of moving average box and Nmax is the dimension of the stochastic series. The ability to capture scaling properties by σMA2 can be understood by observing that the function Cn(i)= y(i)-\widetildeyn(i) generates a sequence of random clusters having power-law probability distribution of the amplitude and of the lifetime, with exponents equal to the fractal dimension D of the stochastic series.