interpret as dynamic fluctuations in brain connectivity can be predicted on the basis of observed functional connectivity estimated over longer time scales. This predictability arises as a consequence of constraints imposed by the use of Pear- son’s correlation to estimate dynamic functional connectivity. For two variables (e.g. regional BOLD signals) to be strongly correlated over long intervals, it must be the case that, on average, they are also strongly correlated over shorter intervals. This relationship becomes stronger as the strength of correlation in- creases, which may explain why the least variable functional connections tend to be the strongest (Gonzalez-Castillo et al., 2014). One possible strategy to help mitigate such issues is to Fisher transform the Pearson correlation coefficients (Fisher, 1915). The Fisher transformation effectively improves the normality of correlation coefficients so that they are no longer bound within the interval [ − 1 , 1]. Thus, as the strength of correlation between two variables increases, their variability stays approximately the same (See Figure S1). However, be- cause the Fisher transform is monotonic the conditional dynamic functional connections estimated from Fisher-transformed data are basically unchanged from those estimated using Pearson’s correlation coefficients (Figure S2). There are other strategies for generating dynamic functional connectivity, in- cluding using non-overlapping windows. In this approach, the full fMRI BOLD time series are segmented into non-overlapping intervals and a connectivity ma- trix created for each window as before. This approach has the obvious advantage that the window at time t is independent of the window at time t + 1. In the supplementary section, we show, qualitatively, that the use of non-overlapping windows to estimate dynamic functional connectivity does not help reduce the dependence of dynamic functional connectivity magnitude on the static cor- relation magnitude. For a single subject we window the 885 TRs into non- overlapping windows of 5, 10, 25, 50, 100, and 200 TRs. We show that in all 25