Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO

TL;DR

This paper introduces a non-asymptotic LASSO-based statistical method for reliably identifying Granger causality in time series data, addressing issues of limited data and confounding noise, with theoretical guarantees and empirical validation.

Contribution

It develops a novel LASSO-based statistic for Granger causality with non-asymptotic analysis, providing fundamental limits and data-driven thresholding methods for improved causal inference.

Findings

The proposed method outperforms traditional OLS in limited data scenarios.

Theoretical bounds on false positive and test power are established.

Simulation and real data experiments validate the method's effectiveness.

Abstract

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.