Long-range temporal and spatial correlations have been reported in a 
remarkable number of studies. A classical approach to analyze this is 
detrended fluctuation analysis (DFA).

The current Malab implementation provides an algorithm not only to quantify
power-law scaling but first to test it against alternatives via (Bayesian)
model comparison.

Like in conventional DFA, after removing (linear or nonlinear) trends of a 
signal, mean squared fluctuations in consecutive intervals are determined.
In contrast to DFA all values per interval are used to approximate the
distribution of these mean squared fluctuations.
This allows for estimating the corresponding log-likelihood as a function
of interval size without presuming the fluctuations to be normally
distributed.

Reference
Ton & Daffertshofer, Model selection for identifying power-law scaling
Neuroimage 136:215-26, 2016, doi:10.1016/j.neuroimage.2016.01.008

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-- main function (we recommend using this wrapper function only

fluctuationAnalysis.m

-- some examples

DFAexamples.m
DFAmoreExamples.m

-- helper functions to generate some time series (used in the examples)

fftfgn.m                generate an fGn sequence with given Hurst exponent
psd2signal.m            generate a signal with given power spectrum
psdfgn.m                generate an fGn with given (set of) Hurst exponent
randomizeFourierPhase.m	randomize the Fourier phase

-- private functions (putting them private improves the overview)

reportDetails.m                 text report + graphics of results
diffusionAnalysis.m             conventional diffusion analysis (SDA)
detrendedFluctuationAnalysis.m	conventional DFA
defineModelCatalogue.m          set the model to compare
detrendedDensities.m            estimate the fluctuation densities
modelSelection.m                non-parametric model comparison (DFA+)
modelSelectionGauss.m           parametric model comparison (DFA-)
	
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All files are released under the terms of the GNU General Public License,
version 3. See http://www.gnu.org/licenses/gpl.html

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Author: Andreas Daffertshofer (a.daffertshofer@vu.nl)