Unveiling change-point detection with ARMA-GARCH models

This paper delves into the asymptotic theory of a Cumulative Sum (CUSUM)-type test designed for detecting change points in the variance of AutoRegressive Moving-Average models, incorporating Generalized Autoregressive Conditional Heteroscedasticity innovations. We demonstrate that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using a Monte Carlo simulation, we highlight the strong performance of our proposed test when compared to the methods by Song and Kang. Furthermore, we provide a real-world data analysis to showcase the practical application of our test.