Uncertainty Assessment and False Discovery Rate Control in High-Dimensional Granger Causal Inference

Causal inference among high-dimensional time series data proves an important research problem in many fields. While in the classical regime one often establishes causality among time series via a concept known as “Granger causality,” exist- ing approaches for Granger causal inference in high-dimensional data lack the means to char- acterize the uncertainty associated with Granger causality estimates (e.g., p-values and confidence intervals). We make two contributions in this work. First, we introduce a novel asymptotically unbiased Granger causality estimator with corre- sponding test statistics and confidence intervals to allow, for the first time, uncertainty characteriza- tion in high-dimensional Granger causal inference. Second, we introduce a novel method for false dis- covery rate control that achieves higher power in multiple testing than existing techniques and that can cope with dependent test statistics and depen- dent observations. We corroborate our theoretical results with experiments on both synthetic data and real-world climatological data.