Simple change point model in heteroscedastic extremes

The framework of heteroscedastic extremes developed by Einmahl et al. (2016) has become an important research area due to its contribution to trend detection. While a previous work of Mefleh et al. (2020) studies some parametric trend models, this article constitutes a small extension to another practical case: the simple change point model where the change point is assumed to be known in time. We first study the model theoretically, estimate the parameter by maximum likelihood method and show its consistency and asymptotic normality. We then associate the proposed model with the discrete log-linear trend model previously developed in Mefleh et al. (2020). We finally verify the results by a simulation and apply the model to real data.