Central Limit Theorem for Weakly Dependent Economic Time Series: Extensions, Error Bounds, and Application to GDP Confidence Intervals

This paper develops a unified probabilistic framework that extends the Classical Central Limit Theorem (CLT) to weakly dependent economic time series exhibiting autocovariance structure. The scientific novelty consists in three contributions: (i) an explicit Berry–Esseen-type bound on the normal approximation error for sequences of the form ; (ii) a long-run variance estimator with a data-adaptive Bartlett–Newey–West kernel and a novel rate-optimal bandwidth selector; (iii) a constructive algorithm for building asymptotically exact GDP confidence intervals under dependent growth-rate innovations, validated on Uzbekistan quarterly national accounts data 2000–2023. All key results are proved rigorously and verified numerically.