Inference on Long-Range Temporal Correlations in Human EEG Data

Rachel J Smith,Beth A Lopour,Daniel W Shrey,Hernando C Ombao

doi:10.1109/jbhi.2019.2936326

Abstract

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.

Highlights

T HE strength of long-range temporal correlations in time series can be estimated by Detrended Fluctuation Analysis (DFA), a statistical method based on scaled windowed variance [1]
When DFA is applied to a segment of time series data, it returns an estimate of the Hurst exponent, but it does not provide a statistical inference for that estimated Hurst exponent
We first confirmed that the resultant scatterplot from DFA was best fit with a linear model, indicating that the amplitude modulations of the time series can accurately be described by power-law scaling

Summary

Introduction

T HE strength of long-range temporal correlations in time series can be estimated by Detrended Fluctuation Analysis (DFA), a statistical method based on scaled windowed variance [1]. Without a quantification of the uncertainty in the estimate of H, within-subject comparisons (across conditions) and the assessment of statistically significant changes in the DFA exponent over time are not possible. We present a statistically rigorous method to estimate the confidence interval for the DFA exponent of human EEG data. This technique enables us to track long-term EEG temporal structure changes in an infant and to compare treatment responses in subjects diagnosed with epilepsy

Methods

Results

Conclusion