Stable Central Limit Theorems for Discrete-Time Lag Martingale Difference Arrays: Applications to Dynamic Causal Inference
离散时间滞后鞅差阵列的稳定中心极限定理及动态因果应用
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain lagged filtrations but not given the natural filtration. We formalize this class of stochastic processes and prove stable central limit theorems (CLTs) via martingale-coboundary decomposition, leveraging the classical martingale CLT. We…