Test for conditional quantile change in GARCH models

In this study, we consider the problem of detecting a change point in the conditional quantile of GARCH models. The task is essential in risk management as the conditional quantile is utilized to calculate the value-at-risk (VaR) of asset prices. We propose the cumulative sum (CUSUM) tests based on the residuals and derive their limiting distributions under mild conditions. We also demonstrate the validity of the tests by conducting Monte Carlo simulations, followed by a real data analysis of the exchange rate between the US Dollar and Korean Won and the Korea composite stock price index.