Standardized-residual-based control charts for simple linear profiles with GARCH errors

Conventional profile monitoring procedures typically assume independent and homoscedastic errors, assumptions that are frequently violated in economic and financial data where volatility clustering is present. When conditional heteroscedasticity arises, standard control charts may exhibit distorted false alarm rates and reduced detection capability. This study develops standardized-residual-based monitoring schemes to detect changes in simple linear profiles with GARCH error structures. The resulting standardized residuals form an approximately independent sequence with unit conditional variance, enabling the application of classical monitoring statistics in a volatility-adjusted setting. Two monitoring schemes are proposed: a standardized-residual-based Hotelling’s T2 chart and a standardized-residual-based EWMA-R chart. Control limits are calibrated through Monte Carlo simulation to achieve a target in-control average run length. Extensive simulation studies evaluate the detection performance of the proposed schemes under intercept, slope, and variance shifts across different GARCH parameter configurations. The results demonstrate that the standardized-residual-based EWMA-R chart provides rapid detection of intercept and slope changes, while the standardized-residual-based T2 chart is sensitive to variance shifts. A case study using hourly Bitcoin–Ethereum price data demonstrates the practical applicability of the framework in volatility-dominated financial environments. The findings highlight that residual-based profile monitoring provides a robust alternative to transformation-based approaches when volatility clustering is present, offering improved detection capability and stable average run length performance under conditional heteroscedasticity.