2024/12/12 by Tian, Yuhan, Abolfazl Safikhani, Safikhani, Abolfazl
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Fault Detection and Control Systems
paper · pdf · doi:10.48550/arxiv.2412.09794
Sequential (online) change-point detection involves continuously monitoring\ntime-series data and triggering an alarm when shifts in the data distribution\nare detected. We propose an algorithm for real-time identification of\nalterations in the transition matrices of high-dimensional vector\nautoregressive models. The algorithm estimates transition matrices and error\nterm variances using regularization techniques applied to training data, then\ncomputes a specific test statistic to detect changes in transition matrices as\nnew data batches arrive. We establish the asymptotic normality of the test\nstatistic under the scenario of no change points, subject to mild conditions.\nAn alarm is raised when the calculated test statistic exceeds a predefined\nquantile of the standard normal distribution. We demonstrate that, as the size\nof the change (jump size) increases, the test power approaches one. The\neffectiveness of the algorithm is validated empirically across various\nsimulation scenarios. Finally, we present two applications of the proposed\nmethodology: analyzing shocks in S&P 500 data and detecting the timing of\nseizures in EEG data.\n