We address the challenge of forecasting counterfactual outcomes in a panel data with missing entries and temporally dependent latent factors -- a common scenario in causal inference, where estimating unobserved potential outcomes ahead of time is essential. We propose Forecasting Counterfactuals under Stochastic Dynamics (FOCUS), a method that extends traditional matrix completion methods by leveraging time series dynamics of the factors, thereby enhancing the prediction accuracy of future counterfactuals. Building upon a consistent estimator of the factors, our method accommodates both stochastic and deterministic components within the factors, and provides a flexible framework for various applications. In case of stationary autoregressive factors and under standard conditions, we derive error bounds and establish asymptotic normality of our estimator. Empirical evaluations demonstrate that our method outperforms existing benchmarks when the latent factors have an autoregressive component. We illustrate FOCUS results on HeartSteps, a mobile health study, illustrating its effectiveness in forecasting step counts for users receiving activity prompts, thereby leveraging temporal patterns in user behavior.

翻译：本文针对面板数据中缺失条目与时间依赖性潜在因子并存情形下的反事实结果预测难题展开研究——这是因果推断中的常见场景，其中提前估计未观测的潜在结果至关重要。我们提出随机动态下的反事实预测方法（FOCUS），该方法通过利用因子的时间序列动态特性扩展了传统矩阵补全方法，从而提升未来反事实的预测精度。基于因子的相合估计量，我们的方法同时容纳因子中的随机性与确定性成分，并为各类应用提供灵活框架。在平稳自回归因子及标准条件下，我们推导了误差界并证明了估计量的渐近正态性。实证评估表明当潜在因子具有自回归成分时，本方法优于现有基准模型。我们通过移动健康研究HeartSteps展示FOCUS的应用效果，说明其在预测接收活动提示用户步数方面的有效性，从而利用用户行为中的时间模式。