Sequential (online) change-point detection involves continuously monitoring time-series data and triggering an alarm when shifts in the data distribution are detected. We propose an algorithm for real-time identification of alterations in the transition matrices of high-dimensional vector autoregressive models. The algorithm estimates transition matrices and error term variances using regularization techniques applied to training data, then computes a specific test statistic to detect changes in transition matrices as new data batches arrive. We establish the asymptotic normality of the test statistic under the scenario of no change points, subject to mild conditions. An alarm is raised when the calculated test statistic exceeds a predefined quantile of the standard normal distribution. We demonstrate that, as the size of the change (jump size) increases, the test power approaches one. The effectiveness of the algorithm is validated empirically across various simulation scenarios. Finally, we present two applications of the proposed methodology: analyzing shocks in S&P 500 data and detecting the timing of seizures in EEG data.

翻译：序贯（在线）变点检测涉及对时间序列数据进行持续监控，并在检测到数据分布发生偏移时触发警报。本文提出一种用于实时识别高维向量自回归模型转移矩阵变化的算法。该算法首先通过应用于训练数据的正则化技术估计转移矩阵与误差项方差，随后在新数据批次到达时计算特定检验统计量以检测转移矩阵的变化。我们在无变点场景下建立了该检验统计量在温和条件下的渐近正态性。当计算得到的检验统计量超过标准正态分布的预设分位数时，系统将触发警报。我们证明随着变化幅度（跳跃规模）的增大，检验功效趋近于一。该算法的有效性通过多种仿真场景得到了实证验证。最后，我们展示了所提方法的两个应用案例：分析标普500数据的冲击效应以及检测脑电图数据中癫痫发作的时点。