  Long-range temporal and spatial correlations have been reported in a
remarkable number of studies. In particular power-law scaling in neural
activity raised considerable interest. We here provide a straightforward
algorithm not only to quantify power-law scaling but to test it against
alternatives using (Bayesian) model comparison. Our algorithm builds on the
well-established detrended fluctuation analysis (DFA). After removing trends of
a signal, we determine its mean squared fluctuations in consecutive intervals.
In contrast to DFA we use the values per interval 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, as is the case in conventional
DFA. We demonstrate the validity and robustness of our algorithm using a
variety of simulated signals, ranging from scale-free fluctuations with known
Hurst exponents, via more conventional dynamical systems resembling
exponentially correlated fluctuations, to a toy model of neural mass activity.
We also illustrate its use for encephalographic signals. We further discuss
confounding factors like the finite signal size. Our model comparison provides
a proper means to identify power-law scaling including the range over which it
is present.
