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 durations to be useful and are not immune to confounding effects. In this work, we close this gap 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 that the sufficient conditions of LASSO also suffice for robust identification of Granger causal influences. We also characterize the false positive error probability of a simple thresholding rule for identifying Granger causal effects. We present simulation studies and application to real data to compare the performance of the ordinary least squares and LASSO in detecting Granger causal influences, which corroborate our theoretical results.

中文翻译：

---

通过LASSO可靠地识别格兰杰因果关系的非渐近保证

格兰杰因果关系是时间序列数据因果分析中广泛使用的数据驱动方法之一，其应用包括经济学，分子生物学和神经科学。这种方法的两个主要挑战是：1）由于数据持续时间有限而导致的过拟合，以及2）将过程噪声作为混淆因素，这两者都导致确定因果关系的错误。通过LASSO进行的稀疏估计已成功解决了参数估计的这些挑战。但是，针对格兰杰因果关系的经典统计检验只能采用渐近分析法对普通最小二乘进行分析，这需要较长的数据持续时间才能发挥作用，并且无法避免产生混淆作用。在这项工作中，我们通过引入基于LASSO的统计数据并在真实模型允许稀疏自回归表示的假设下研究其非渐近性质来弥合这一差距。我们确定，LASSO的充分条件也足以可靠地识别格兰杰因果影响。我们还表征了用于识别格兰杰因果效应的简单阈值规则的假正错误概率。我们目前进行仿真研究并将其应用于实际数据，以比较普通最小二乘法和LASSO在检测格兰杰因果影响方面的性能，从而证实了我们的理论结果。我们还表征了用于识别格兰杰因果效应的简单阈值规则的假正错误概率。我们目前进行仿真研究并将其应用于实际数据，以比较普通最小二乘法和LASSO在检测格兰杰因果影响方面的性能，从而证实了我们的理论结果。我们还表征了用于识别格兰杰因果效应的简单阈值规则的假正错误概率。我们目前进行仿真研究并将其应用于实际数据，以比较普通最小二乘法和LASSO在检测格兰杰因果影响方面的性能，从而证实了我们的理论结果。