Long term correlation analysis (LTCA)
Purpose
Description
Macro Synopsis
Modules
Related Functions
References
Purpose
Long term correlation analysis
Description
"Long term correlation analysis (LTCA)" detects the characteristics of fractal noise. It examines
the long-term correlations in the given signal x by finding the
mean-square fluctuation function
:
with
where the horizontal bar denotes averages.
The result can be interpreted as follows:
- if
, there are correlations up to a
characteristic distance R, but the asymptotic behaviour is similar to the purely random case;
- if
, there are "infinite-range" correlations
and the signal is fractal, as long as 
;
- If
, the signal is similar to a random walk;
the log-log plot of F(l) approximates a straight line with slope 0.5.
This function is a modified version of the so-called R/S or Hurst analysis.
Macro Synopsis
y = LTCA(x);
signal x,y;
Modules
Statistics
Related Functions
Box-Cox transform, Detrended fluctuation analysis (DFA),
Exponential regression, Fractal noise, Linear regression,
Multilinear regression, Power regression,
Principal component analysis (PCA), R/S statistics, Remove DC,
Remove trend.
References
Mandelbrot [30], Karrakchou et al. [39]