Yuan, A. E. | Search bioRxiv

bioRxiv2022

An exactly valid and distribution-free statistical significance test for correlations between time series

In disciplines from biology to climate science, a routine task is to compute a correlation between a pair of time series, and determine whether the correlation is statistically significant (i.e. unlikely under the null hypothesis that the time series are independent). This problem is challenging because time series typically exhibit autocorrelation, which cannot be properly analyzed with the standard iid-oriented statistical tests. Although there are well-known parametric tests for time series, these are designed for linear correlation statistics and thus not suitable for the increasingly popular nonlinear correlation statistics. Among nonparametric tests, the conditions that guarantee correct false positive rates are either restrictive or unclear. Here we describe the truncated time-shift (TTS) test, a nonparametric procedure to test for dependence between two time series. We prove that this test is valid as long as one of the time series is stationary, a minimally restrictive requirement among current tests. The TTS test is versatile because it can be used with any correlation statistic. Using synthetic data, we demonstrate that this test performs correctly even while other tests suffer high false positive rates. In simulation examples, simple guidelines for parameter choices allow high statistical power to be achieved with sufficient data. We apply the test to data sets from climatology, animal behavior and microbiome science, verifying previously discovered dependence relationships and detecting additional relationships.

bioinformatics↗

bioRxiv2020

Data-driven causal analysis of observational time series: a synthesis

Complex ecosystems are challenging to understand as they often defy manipulative experiments for practical or ethical reasons. In response, several fields have developed parallel approaches to infer causal relations from observational time series. Yet these methods are easy to misunderstand and often controversial. Here, we provide an accessible and critical review of three statistical causal inference approaches popular in ecological time series analysis: pairwise correlation, Granger causality, and state space reconstruction. For each, we ask what a method tests for, what causal statement it might imply, and when it could lead us astray. We devise new ways of visualizing key concepts, describe some novel pathologies of causal inference methods, and point out how so-called "model-free" causality tests are not assumption-free. We hope that our synthesis will facilitate thoughtful application of causal inference approaches and encourage explicit statements of assumptions.

bioinformatics↗