Let Time Tell: Identification and Gaussian Process Estimation for Interrupted Time Series

• URL: http://arxiv.org/abs/2608.20610v1
• Date: Thu, 20 Aug 2026 23:20:16 GMT
• Title: Let Time Tell: Identification and Gaussian Process Estimation for Interrupted Time Series
• Abstract summary: We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously.<n>We establish identification within the potential outcomes framework and estimate the counterfactual by Gaussian process regression.<n>An R package, gpss, implements the approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously, so that the contemporaneous controls used by difference-in-differences and synthetic control are unavailable and the counterfactual must be extrapolated from a unit's own pre-treatment history. We establish identification within the potential outcomes framework and estimate the counterfactual by Gaussian process regression. Rather than committing to a single best-fitting trend, the estimator retains the functions consistent with the pre-treatment series and widens its intervals where extrapolation magnifies their divergence. Connecting it to reproducing kernel Hilbert space theory, we derive a bias decomposition that isolates the component extrapolation inflates and a worst-case bound on that component, justifying the Gaussian process estimator's posterior variance as extrapolation-aware uncertainty quantification. In closed form, the band equals the worst-case divergence the model class permits among functions consistent with the pre-treatment data. The method is illustrated with calibrated simulations and an analysis of handgun purchases after the Supreme Court's Heller decision, a universal treatment whose practical effect concentrates in a single jurisdiction. An R package, gpss, implements the approach.

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