DecoR : deconfounding time series with robust regression

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2026 · Volume 88 · Issue 3

Abstract

Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. In this work, we focus on estimating the causal effect of a multivariate time series on a univariate time series when a third (possibly multivariate) time series confounds the relationship but remains unobserved. By assuming spectral sparsity of the confounder, we show how this problem can be framed as an adversarial outlier problem in the frequency domain. We introduceDeconfounding byRobust regression (DecoR), a novel approach that estimates the causal effect using robust linear regression in the frequency domain. We consider two robust regression techniques and provide improved bounds on their estimation errors. Applying these results toDecoR, we prove, under suitable assumptions, upper bounds for the estimation error ofDecoRthat imply consistency. We demonstrateDecoR’s effectiveness through experiments on both synthetic and real-world data from Earth system science. The simulation experiments furthermore suggest thatDecoRis robust with respect to model misspecification.

Keywords

causal inference, confounding, earth system science, robust regression, time series analysis

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