Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using contemporaneous outcomes in control units. Methodological developments here concern multivariate dynamic models for time-varying effects across multiple treated units with explicit foci on sequential learning and aggregation of intervention effects. Analysis explores dimension reduction across multiple synthetic counterfactual predictors. Computational advances leverage fully conjugate models for efficient sequential learning and inference, including cross-unit correlations and their time variation. This allows full uncertainty quantification on model hyper-parameters via Bayesian model averaging. A detailed case study evaluates interventions in a supermarket promotions experiment, with coupled predictive analyses in selected regions of a large-scale commercial system. Comparisons with existing methods highlight the issues of appropriate uncertainty quantification in casual inference in aggregation across treated units, among other practical concerns.

翻译：本文在多元时间序列分析中发展了贝叶斯预测方法以进行因果推断。对来自对照组和处理组的顺序观测时间序列数据的因果评估，重点关注利用对照组同期结果来评估干预措施的影响。方法论上的进展涉及针对多个处理单元时变效应的多元动态模型，明确聚焦于干预效应的序贯学习与聚合分析。研究探索了跨多个合成反事实预测变量的降维方法。计算上的进步利用了完全共轭模型来实现高效的序贯学习与推断，包括跨单元相关性及其时变特性。这使得能够通过贝叶斯模型平均对模型超参数进行完整的不确定性量化。详细的案例研究评估了超市促销实验中的干预措施，并在大规模商业系统的选定区域进行了耦合预测分析。与现有方法的比较突显了在处理单元聚合的因果推断中进行适当不确定性量化的问题，以及其他实际考量。