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Detrended Fluctuation Analysis (DFA) is widely used to assess the presence oflong-range temporal correlations in time series. Signals with long-rangetemporal correlations are typically defined as having a power law decay intheir autocorrelation function. The output of DFA is an exponent, which is theslope obtained by linear regression of a log-log fluctuation plot againstwindow size. However, if this fluctuation plot is not linear, then theunderlying signal is not self-similar, and the exponent has no meaning. Thereis currently no method for assessing the linearity of a DFA fluctuation plot.Here we present such a technique, called ML-DFA. We scale the DFA fluctuationplot to construct a likelihood function for a set of alternative modelsincluding polynomial, root, exponential, logarithmic and spline functions. Weuse this likelihood function to determine the maximum likelihood and thus tocalculate values of the Akaike and Bayesian information criteria, whichidentify the best fit model when the number of parameters involved is takeninto account and over-fitting is penalised. This ensures that, of the modelsthat fit well, the least complicated is selected as the best fit. We applyML-DFA to synthetic data from FARIMA processes and sine curves with DFAfluctuation plots whose form has been analytically determined, and toexperimentally collected neurophysiological data. ML-DFA assesses whether thehypothesis of a linear fluctuation plot should be rejected, and thus whetherthe exponent can be considered meaningful. We argue that ML-DFA is essential toobtaining trustworthy results from DFA.

A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)