  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.
