## Detrended fluctuation analysis (DFA)

Purpose

Description

Tips

Macro Synopsis

Modules

Related Functions

References

### Purpose

Detrended fluctuation analysis

### Description

"Detrended fluctuation analysis (DFA)" gives a measure of the time-dependent fluctuations in a signal.
After a linear trend removal, the standard deviation of the detrended time series up to a signal length l is calculated and plotted against l.

### Tips

A log/log-plot of the output signal yields the exponents of fluctuation-length-dependency.

### Macro Synopsis

`y = DFA(x);`

signal x,y;

### Modules

Statistics

### Related Functions

Box-Cox transform, Exponential regression,
Linear regression, Long term correlation analysis (LTCA),
Multilinear regression, Power regression,
Principal component analysis (PCA), R/S statistics, Remove DC,
Remove trend.

### References

Peng et al. [26]