A0507
Title: A nonparametric test for correlation between nonstationary time series: Addressing challenges with limited replicates
Authors: Alex Yuan - University of Washington (United States) [presenting]
Wenying Shou - University College London (United Kingdom)
Abstract: In disciplines from ecology to neuroscience, researchers analyze correlations between pairs of nonstationary time series to infer interactions or shared influences among variables. This often involves testing whether an observed correlation is stronger than expected under the null hypothesis that time series are independent. With only one experimental replicate, testing for dependence between nonstationary time series is exceedingly challenging and generally requires strong assumptions. Conversely, with many replicates, a nonparametric trial-swapping permutation test can be used where within-replicate correlations are compared to between-replicate correlations. Although this test is largely assumption-free, its minimum achievable p-value is $1/n!$ (where $n$ is the number of replicates), making significance thresholds like 0.05 unattainable when $n \leq 3$. A variant of this approach that can report lower p-values of $2/n^n$ or $1/n^n$ when there is strong evidence of dependence is described. This is useful for biomedical studies, where $n$ is often $3 \sim 5$, limiting the significance obtained by permutation alone. The test prevents the false positive rate from exceeding the significance level and only requires that replicates are independent and identically distributed. The test is demonstrated by confirming the observation that groups of zebrafish swim faster when directionally aligned, using a public dataset with three biological replicates.
