Detecting Mean Shifts in a Class of Time Series CHARN Models with Application to Financial Data

In this paper, we propose a fully automated method for detecting changes in the mean of piecewise Conditional Heteroskedastic Autoregressive Nonlinear (CHARN) models. Detecting weak changes, those of small magnitude, is crucial in financial and economic applications, where they may signal important structural breaks. Our approach combines an adaptive model selection algorithm with a robust break detection procedure based on local power estimation. By dynamically selecting the most appropriate model for each stationary segment, the method reduces false alarms and improves sensitivity to subtle transitions. Applied to financial datasets such as the S&P 500 and FTSE 100 indices, the algorithm operates automatically and not only reproduces known breakpoints documented in the literature, but also uncovers previously undetected structural changes. These additional findings correspond to meaningful real-world events, highlighting the effectiveness and reliability of the proposed framework for analyzing financial time series and its potential value for financial stability, trading strategies, and risk management.