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, which 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 show DecoR's effectiveness through experiments on synthetic data. Our experiments furthermore suggest that our method 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。假设混杂因子具有频谱稀疏性，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来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，我们的结果不要求对协变量进行分布假设。因此，我们可以在时间序列设置中使用它们。将这些结果应用于DecoR，我们在适当的假设下证明了DecoR估计误差的上界，该上界蕴含了一致性。我们通过在合成数据上的实验展示了DecoR的有效性。此外，我们的实验表明，我们的方法对于模型误设定具有鲁棒性。