One-class classification-based monitoring for the mean and variance of time series

This study develops a statistical process control (SPC) chart that simultaneously monitors the mean and variance of general location-scale time series models. Integrating the one-class classification (OCC) technique (the support vector data description (SVDD) particularly), we formulate a nonlinear boundary to enclose in-control observations for detecting structural anomalies. The control limits obtained from SVDD can capture a more sophisticated structural change and are also controllable. We particularly propose a control chart formulated using location-scale residuals. This further enhances our ability to detect shifts in the mean, variance, and various model parameters. The proposed OCC control chart is compared with some traditional charts and is validated by conducting simulations under various circumstances. Moreover, we consolidate applicability in a real data analysis by demonstrating its functionality with the S&P 500 index.