There is increasing interest in detecting collective anomalies: potentially short periods of time where the features of data change before reverting back to normal behaviour. We propose a new method for detecting a collective anomaly in VAR models. Our focus is on situations where the change in the VAR coefficient matrix at an anomaly is sparse, i.e. a small number of entries of the VAR coefficient matrix change. To tackle this problem, we propose a test statistic for a local segment that is built on the lasso estimator of the change in model parameters. This enables us to detect a sparse change more efficiently and our lasso-based approach becomes especially advantageous when the anomalous interval is short. We show that the new procedure controls Type 1 error and has asymptotic power tending to one. The practicality of our approach is demonstrated through simulations and two data examples, involving New York taxi trip data and EEG data.
翻译:发现集体异常现象的兴趣越来越大:数据特征在恢复到正常行为之前发生变化的时间可能很短;我们提出了在VAR模型中发现集体异常现象的新方法;我们的重点是异常点VAR系数矩阵变化稀少的情况,即VAR系数矩阵变化的少量条目;为解决这一问题,我们建议对建在模型参数变化的拉索估计符上的局部部分进行测试统计;这使我们能够更高效地发现少许变化,在异常点间隔短时,我们基于套索的方法变得特别有利;我们表明,新的程序控制类型1错误,其零耗能力倾向于一种。我们的方法的实用性通过模拟和两个数据实例,包括纽约出租车旅行数据和EEG数据,得到证明。