Sequential Change Point Detection in High-dimensional Vector Auto-regressive Models

Abstract: 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.