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

Abstract

This study proposes a control chart that monitors conditionally heteroscedastic time series by integrating the Huber support vector regression (HSVR) and the one-class classification (OCC) method. For this task, we consider the model that incorporates nonlinearity to the generalized autoregressive conditionally heteroscedastic (GARCH) time series, named HSVR-GARCH, to robustly estimate the conditional volatility when the structure of time series is not specified with parameters. Using the squared residuals, we construct the OCC-based control chart that does not require any posterior modifications of residuals unlike previous studies. Monte Carlo simulations reveal that deploying squared residuals from the HSVR-GARCH model to control charts can be immensely beneficial when the underlying model becomes more complicated and contaminated with noises. Moreover, a real data analysis with the Nasdaq composite index and Korea Composite Stock Price Index (KOSPI) datasets further disclose the validity of using the bootstrap method in constructing control charts.