Detection and Localization of Multi-Type Parameter Changes in Non-Stationary Data

This paper studies a common but complex change-point setting in time series, where a smoothly evolving mean trend may coexist with abrupt shifts in both the mean and variance. To address this joint problem in such complex non-stationary data, we propose a novel iterative estimation procedure that alternates between smoothing-spline estimation of the mean function and likelihood-ratio tests for mean and variance change-points. The resulting method jointly estimates the mean change-point and the jump size of the mean shift, the two smooth mean functions before and after the change-point, the variance change-point, and the variances before and after the change. We derive the asymptotic null distributions of the proposed test statistics and establish convergence rates for the estimators of the smooth mean functions, change-point locations, mean shift size, and variance parameters. Simulation studies and a real-data application demonstrate that the proposed procedure is stable across a range of settings and provides accurate change-point detection together with reliable trend estimation. The proposed method is computationally tractable and has potential applications in finance, meteorology, sensor monitoring, economics, and industrial process control.