Workshop on Methods of Information Theory in Computational NeuroscienceOliver CliffThe University of Sydney
Exact Inference of Linear Dependence Between Multiple Autocorrelated Time Series
Inferring linear dependence between time series is central to the study of dynamics, and has significant consequences for our understanding of natural and artificial systems. Unfortunately, traditional hypothesis tests often yield spurious associations (type I errors) or omit causal relationships (type II errors) when used to infer directed or multivariate dependencies in time-series data. Here we show that this problem is due to autocorrelation in the analysed time series -- a property that is ubiquitous across a diverse range of applications, from brain dynamics to climate change, and can be exacerbated by digital filtering. This insight enabled us to derive the first exact hypothesis tests for a large family of multivariate linear-dependence measures, including Granger causality and mutual information. Using numerical simulations and fMRI brain recordings, we show that our tests maintain the expected false-positive rate with minimally-sufficient samples, while demonstrating that asymptotic likelihood-ratio tests can induce unbounded statistical errors. Our findings suggest that many time-series dependencies in the scientific literature may have been, and may continue to be, spuriously reported or missed if our testing procedure is not widely adopted. (Cliff et al., arXiv:2003.03887)
