An Association Framework to Analyze Dependence Structure in Time Series

Abstract

The purpose of this paper is two-fold: first, to propose a modification to the generalized measure of association (GMA) framework that reduces the effect of temporal structure in time series; second, to assess the reliability of using association methods to capture dependence between pairs of EEG channels using their time series or envelopes. To achieve the first goal, the GMA algorithm was updated so as to minimize the effect of the correlation inherent in the time structure. The reliability of the modified scheme was then assessed on both synthetic and real data. Synthetic data was generated from a Clayton copula, for which null hypotheses of uncorrelatedness were constructed for the signal. The signal was processed such that the envelope emulated important characteristics of experimental EEG data. Results show that the modified GMA procedure can capture pairwise dependence between generated signals as well as their envelopes with good statistical power. Furthermore, applying GMA and Kendall's tau to quantify dependence using the extracted envelopes of processed EEG data concords with previous findings using the signal itself.