Sequential monitoring for conditional quantiles of general conditional heteroscedastic time series models

Abstract

In this study, we introduce an online monitoring procedure designed to sequentially detect change points in the conditional quantiles of location-scale time series models. This statistical process control issue holds great significance in risk management, particularly in measuring the value-at-risk or expected shortfall of financial assets. Our approach employs suitable detectors, including cumulative sum statistics. We then define a stopping rule and determine control limits based on asymptotic theorems to signal an anomaly. To further evaluate the proposed methods, we conduct a comprehensive empirical study analyzing various aspects of our monitoring procedures when applied to location-scale time series models. Additionally, we perform a real data analysis using the daily returns of the Korea Composite Stock Price Index (KOSPI) and EuroStoxx 50 indices to affirm the adequacy of the proposed monitoring procedures in real-world applications.