Estimating the Effects of Interventions in Multivariate Time Series Settings

Abstract

This article addresses the methodological challenge of estimating the causal effects of interventions in time series settings where multiple interrelated outcomes may be present. Many real-world applications involve multiple correlated indicators or outcomes—for instance, economic variables reflecting different but interdependent aspects of economic performance, or various epidemiological measures tracking health outcomes. This study reviewed classical univariate factor models (FA) and highlighted their strengths and limitations in isolating intervention impacts under potentially confounded environments. Subsequently, we explore multivariate extensions Factor Analysis (MVFA) that employ shared and outcome-specific latent factors to handle correlations across multiple time series. Building on recent developments, we discuss the Causal ARIMA (C-ARIMA) framework which integrates ARIMA-based structures with potential-outcomes theory, and the Bayesian Multivariate Factor Analysis approach that leverages shrinkage priors and Markov chain Monte Carlo (MCMC) inference for robust estimation of counterfactual trajectories. Simulation evidence and practical considerations suggest these methods can outperform simpler alternatives (e.g., traditional regression or difference-in-differences) when data exhibit hidden confounders, time-varying shocks, or small sample sizes. Overall, the article provides a consolidated view of modern techniques for intervention analysis in complex time series, emphasizing both theoretical motivations and applied utility.