Scaling Properties of Long-Range Correlated Noisy Signals

Abstract

The Hurst coefficient $H$ of a stochastic fractal signal is estimated using the function ${\sigma }_{MA}^2=\frac{1}{N_{max}-n}{\sum }_{i=n}^{N_{max}}[y(i)-{\tilde{y}}_n(i){]}^2$, where ${\tilde{y}}_n(i)$ 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 $C_n(i)=y(i)-{\tilde{y}}_n(i)$ 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.

9 pages, 4 figures, submitted to Physical Review E

Cited by in corpus (1)

• Review of Nonlinear Methods and Modelling