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.

中文翻译：

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人类脑电数据中长期时间相关性的推论。

去趋势波动分析（DFA）是一种统计估计算法，用于评估神经时间序列中的长期时间依赖性。该算法产生一个DFA指数，该数字反映了数据中长期时间相关性的强度。尚未开发任何方法来为单个时间序列段生成DFA指数的置信区间。因此，我们通过应用移动块自举（MBB），提出了脑电图（EEG）数据中DFA指数不确定性的统计度量。我们测试了三个数据特征对DFA指数的影响：（1）时间序列长度，（2）伪像的存在，以及（3）不连续的存在。我们发现〜5分钟的信号长度产生了DFA指数的稳定测量值，并且伪像的存在正偏DFA指数分布。相比之下，不连续的影响很小，即使与去除伪影有关的影响也很小。我们表明，可以将移动块自举程序与DFA结合使用以获得DFA指数及其在模拟数据和人类EEG数据中的相关置信区间的准确估计。我们将拟议的方法应用于人类脑电图数据，以（1）计算健康婴儿的睡眠-觉醒周期中长期时间依赖性的时变估计，以及（2）比较个体内治疗前和治疗后脑电图数据小儿癫痫患者。