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.
Peng et al. introduced DFA in 1994 in a paper that has been cited over 3,000 times as of 2022[1] and represents an extension of the (ordinary) fluctuation analysis (FA), which is affected by non-stationarities.
^Peng, C.K.; et al. (1994). "Mosaic organization of DNA nucleotides". Phys. Rev. E. 49 (2): 1685–1689. Bibcode:1994PhRvE..49.1685P. doi:10.1103/physreve.49.1685. PMID 9961383. S2CID 3498343.
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