ABSTRACT

We focus on sequential (online) monitoring of changes in the mean vector of high-dimensional persistent VARMA time series by using multivariate control charts. Applying either modified or residual control charts to the original process or to the process of VARMA residuals could be problematic when the degree of autoregressive persistence is high. To overcome these difficulties, we suggest to monitor the process of the vector first differences of the VARMA series. We derive the stochastic properties of this difference vector process which are required for the design of the multivariate control charts. Then, we illustrate the performance of our approach in a Monte Carlo simulation study for detection of various types of mean changes.

摘要

我们专注于使用多元控制图对高维持久 VARMA 时间序列的平均向量的变化进行顺序（在线）监控。当自回归持久性程度很高时，将修改后或残差控制图应用于原始过程或 VARMA 残差过程可能会出现问题。为了克服这些困难，我们建议监控 VARMA 级数的向量一阶差分的过程。我们推导出这种差异向量过程的随机特性，这是设计多元控制图所必需的。然后，我们说明了我们的方法在蒙特卡罗模拟研究中的性能，用于检测各种类型的平均变化。