发表机构
University College London; University of Cambridge（伦敦大学学院; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间序列中格兰杰因果检验，提出无模型的条件独立性检验方法GTCM，通过非线性回归与残差协方差统计量，在弱假设下控制错误率并利用全数据估计。
AI 中文摘要
我们考虑时间序列中检验格兰杰因果关系的问题，具体而言，即未来结果 $Y_{t+1}$ 与暴露历史 $\ar X_t$ 在给定 $\ar Y_t$ 的历史以及截至时间 $t$ 的一组混杂变量 $\ar Z_t$ 的条件下是否条件独立。该检验程序将真正的因果效应与由共同外部过程驱动的关联区分开来，为金融、神经科学和气候科学等应用中的可靠决策提供支持。虽然传统方法假设线性向量自回归（VAR）模型，并且容易受到设定错误的影响，我们转而处理该问题的无模型版本。我们提出对结果和暴露分别关于 $Y$ 和 $Z$ 的联合历史进行非线性回归，并基于残差的样本协方差计算检验统计量，我们称之为广义时间协方差度量（GTCM）。为了考虑异方差性并提高对局部备择假设的功效，我们纳入方差权重，并采用基于多项式滞后的数据自适应检验。该检验的 I 类错误控制依赖于一个相对较弱的假设，即用户选择的回归过程以足够快的速度估计条件均值，该速度慢到足以适应非参数设置。通过进一步假设回归过程的稳定性和时间序列的弱依赖性，我们可以利用整个数据集来估计条件均值，而无需将时间序列分割成子集。
英文摘要
We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects from associations driven by common external processes, supporting reliable decision-makings in applications such as finance, neuroscience, and climate science. While traditional approaches assume a linear vector autoregressive (VAR) model and are vulnerable to misspecification, we instead address a model-free version of the problem. We propose nonlinearly regressing both the outcome and exposure on the joint history of $Y$ and $Z$, and calculating a test statistic based on the sample covariance of residuals, we call the Generalised Temporal Covariance Measure (GTCM). To account for heteroscedasticity and improve power against local alternatives, we incorporate variance weights and employ a data-adaptive test based on polynomial lag expansions.The type I error control of the test relies on the relatively weak assumption that user-chosen regression procedures estimate conditional means at a sufficiently fast rate that is slow enough to accommodate nonparametric settings. By further assuming stability of the regression procedures and weak dependence in the time series, we can utilise the entire dataset to estimate the conditional means without splitting the time series into subsets.
Comments31 pages, 2 figures, 1 table
