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= 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 an estimation of 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 2020[1] and represents an extension of the (ordinary) fluctuation analysis (FA), which is affected by non-stationarities.

Neuroscience
DFA has also been used recently in the field of Neuroimaging in studies of both Functional dynamics, the study of brain activity over time, and Functional connectivity, the study of how the brain is connected through the co-activation of different brain regions at a given point in time. DFA is used to estimate the Hurst exponent for every Voxel of the brain as a means of capturing it's intrinsic activity in a single number quantifying the properties of the signal and it's Fractal nature. Although DFA cannot be used to infer if the co-activation between two or more brain regions is the result of chance finding or a genuine functional connection, it can still allow for the study of brain activity specifically the properties of this activity based on the Hurst exponent estimated for each Voxel. This approach may be useful in Neuroimaging as it can drastically reduce the number of statistical tests required for a full brain analysis decreasing the likelihood of conducting a type II error, or missing important findings due to a lack of Statistical power.

Studies that used DFA have found that at rest and during sleep, the Hurst exponent values are highest in regions part of the Default mode network however, when an individual engages in a task, the Hurst exponent decreases in relation to those found at rest. This suggests that during a task, brain activity shifts from pin noise to white noise in other words, the temporal profile of a brain signal changes from being serially auto-correlated to being uncorrelated. This nature of this change or the interpretation of this change in observed Hurst exponent values has yet to be fully explored and remains a growing field of scientific study.