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

Abstract

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.

Robust control chart for nonlinear conditionally heteroscedastic time series based on Huber support vector regression

“…In this subsection, we report the results of three experiments as follows. First, we compare the performance of our proposed OCC-based control chart with that of [47] by comparing control charts constructed from either �2 t or �2 t , where the latter denotes the residuals employed in [47]. For fairness, we consider the control charts constructed from HSVR-GARCH residuals for both models to avoid the model misspecification issue in this particular experiment.…”

“…For a class of parametric GARCH models, [46] studied the estimation of their parameters and presented a method of conducting the change point test as an application. Their research later offered a theoretical foundation that based the OCC control charts of [47].…”

“…Although the general procedure to construct the OCC-based control chart in this study resembles those of [47], our OCC-based control chart is designed to preserve the original structure of the given time series compared to the latter. In implementation, OCC charts of [47] must sequentially perform the Yeo-Johnson transformation and the moving-average smoothing to the residuals to alleviate the instability caused by the inaccurate estimation of the model parameters.…”

“…Although the general procedure to construct the OCC-based control chart in this study resembles those of [47], our OCC-based control chart is designed to preserve the original structure of the given time series compared to the latter. In implementation, OCC charts of [47] must sequentially perform the Yeo-Johnson transformation and the moving-average smoothing to the residuals to alleviate the instability caused by the inaccurate estimation of the model parameters. Despite these efforts, OCC charts had a relatively inferior performance in terms of ARL 1 compared to other charts, such as CUSUM or EWMA charts, when monitoring the conditional volatility using squared residuals, see Section 4 of [47].…”

“…In implementation, OCC charts of [47] must sequentially perform the Yeo-Johnson transformation and the moving-average smoothing to the residuals to alleviate the instability caused by the inaccurate estimation of the model parameters. Despite these efforts, OCC charts had a relatively inferior performance in terms of ARL 1 compared to other charts, such as CUSUM or EWMA charts, when monitoring the conditional volatility using squared residuals, see Section 4 of [47]. Furthermore, as our simulation study indicates, smoothing residuals undermines the overall detection ability when the underlying model is contaminated with noises, see Section 4 of this paper for more detail.…”