Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. This work focuses on estimating the causal effect between two time series that are confounded by a third, unobserved time series. Assuming spectral sparsity of the confounder, we show how in the frequency domain this problem can be framed as an adversarial outlier problem. We introduce Deconfounding by Robust regression (DecoR), a novel approach that estimates the causal effect using robust linear regression in the frequency domain. Considering two different robust regression techniques, we first improve existing bounds on the estimation error for such techniques. Crucially, our results do not require distributional assumptions on the covariates. We can therefore use them in time series settings. Applying these results to DecoR, we prove, under suitable assumptions, upper bounds for the estimation error of DecoR that imply consistency. We demonstrate DecoR's effectiveness through experiments on both synthetic and real-world data from Earth system science. The simulation experiments furthermore suggest that DecoR is robust with respect to model misspecification.

翻译：时间序列数据上的因果推断是一个具有挑战性的问题，尤其是在存在未观测混杂因子的情况下。本研究聚焦于估计两个时间序列之间的因果效应，这两个序列受到第三个未观测时间序列的混杂。假设混杂因子具有谱稀疏性，我们证明了在频域中该问题可被构建为一个对抗性离群值问题。我们提出了基于鲁棒回归的去混杂方法（DecoR），这是一种在频域中使用鲁棒线性回归估计因果效应的新方法。通过考虑两种不同的鲁棒回归技术，我们首先改进了此类技术估计误差的现有界。关键的是，我们的结果不需要对协变量进行分布假设，因此可将其应用于时间序列场景。将这些结果应用于DecoR，我们在适当假设下证明了DecoR估计误差的上界，该上界蕴含了一致性。我们通过地球系统科学的合成数据与真实数据实验验证了DecoR的有效性。仿真实验进一步表明DecoR对模型误设具有鲁棒性。