Scaling Properties of Long-Range Correlated Noisy Signals
Abstract
The Hurst coefficient
H
of a stochastic fractal signal is estimated using the function
σ
2
MA
=
1
N
max
−n
∑
N
max
i=n
[y(i)−
y
˜
n
(i)
]
2
, where
y
˜
n
(i)
is defined as
1/n
∑
n−1
k=0
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
σ
2
MA
can be understood by observing that the function
C
n
(i)=y(i)−
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.