**Detrended Fluctuation Analysis**

In stochastic processes, chaos theory and time series analysis, **detrended fluctuation analysis (DFA)** is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.

The obtained exponent is similar to the Hurst exponent, except that DFA may also be applied to signals whose underlying statistics (such as mean and variance) or dynamics are non-stationary (changing with time). It is related to measures based upon spectral techniques such as autocorrelation and Fourier transform.

DFA was introduced by Peng et al. 1994 and represents an extension of the (ordinary) fluctuation analysis (FA), which is affected by non-stationarities.

Read more about Detrended Fluctuation Analysis: Calculation, Relations To Other Methods, Pitfalls in Interpretation

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**Detrended Fluctuation Analysis**- Pitfalls in Interpretation

... Also, there are many scaling exponent-like quantities that can be measured for a self-similar time series, including the divider dimension and Hurst exponent ... Therefore, the DFA scaling exponent is not a fractal dimension sharing all the desirable properties of the Hausdorff dimension, for example, although in certain special cases it can be shown to be related to the box-counting dimension for the graph of a time series ...

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