## 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]