This paper focuses on testing and estimating abrupt change-point in volatility for a specific class of parametric Autoregressive Conditional Heteroscedastic models, referred to as \(\beta \) -ARCH(1). We initially establish a \(\beta \) -ARCH(1)’s parameters estimator, which is based on the Minimum Hellinger Distance (MHD). Subsequently, we propose a Kolmogorov-Smirnov type test for volatility change-point in \(\beta \) -ARCH(1) model, and we construct an estimator of the volatility change-point location. The asymptotic distribution of our test statistic under the null hypothesis is then explored, followed by an affirmation of our estimator’s consistency. To validate our approaches, simulations on \(\beta \) -ARCH(1) models under varying noise distributions (Gaussian and Gumbel) confirm the consistency and robustness of both the MHD parameter estimator and the volatility change-point location estimator, which were evaluated in terms of bias and standard error. Comparative simulations–benchmarking our volatility change-point estimation approach against three recent algorithms (WBS, NOT, and ICSS) using simulated data–show that it yields lower bias, particularly for subtle volatility shifts. An empirical application to RUB/GBP exchange-rate data highlights our method’s practical superiority in volatility change detection compared with these alternatives.
