  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.
