Inference on Long-Range Temporal Correlations in Human EEG Data

Detrended Fluctuation Analysis (DFA) is a statistical estimation algorithm used to assess long-range temporal dependence in neural time series. The algorithm produces a single number, the DFA exponent, that reflects the strength of long-range temporal correlations in the data. No methods have been developed to generate confidence intervals for the DFA exponent for a single time series segment. Thus, we present a statistical measure of uncertainty for the DFA exponent in electroencephalographic (EEG) data via application of a moving-block bootstrap (MBB). We tested the effect of three data characteristics on the DFA exponent: (1) time series length, (2) the presence of artifacts, and (3) the presence of discontinuities. We found that signal lengths of ~5 minutes produced stable measurements of the DFA exponent and that the presence of artifacts positively biased DFA exponent distributions. In comparison, the impact of discontinuities was small, even those associated with artifact removal. We show that it is possible to combine a moving block bootstrap with DFA to obtain an accurate estimate of the DFA exponent as well as its associated confidence intervals in both simulated data and human EEG data. We applied the proposed method to human EEG data to (1) calculate a time-varying estimate of long-range temporal dependence during a sleep-wake cycle of a healthy infant and (2) compare pre- and post-treatment EEG data within individual subjects with pediatric epilepsy. Our proposed method enables dynamic tracking of the DFA exponent across the entire recording period and permits within-subject comparisons, expanding the utility of the DFA algorithm by providing a measure of certainty and formal tests of statistical significance for the estimation of long-range temporal dependence in neural data.