Scaling Properties of Long-Range Correlated Noisy Signals

Details Scaling Properties of Long-Range Correlated Noisy Signals Scaling Properties of Long-Range Correlated Noisy Signals

2003-03-21

arxiv.org/abs/cond-mat/0303465v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 figures, submitted to Physical Review E

Scientific paper

The Hurst coefficient $H$ of a stochastic fractal signal is estimated using the function $\sigma_{MA}^2=\frac{1}{N_{max}-n}\sum_{i=n}^{N_{max}} [y(i)-\widetilde{y}_n(i)]^2$, where $\widetilde{y}_n(i)$ is defined as $1/n \sum_{k=0}^{n-1} y(i-k)$, $n$ is the dimension of moving average box and $N_{max}$ is the dimension of the stochastic series. The ability to capture scaling properties by $\sigma_{MA}^2$ can be understood by observing that the function $C_n(i)= y(i)-\widetilde{y}_n(i)$ 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.

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