Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series model, while the latter employs (locally) time-varying models to describe smooth changes in dependence structure of a time series. However, in some applications, abrupt and smooth changes can co-exist, and neither of the two approaches alone can model the data adequately. In this paper, we propose a novel likelihood-based procedure for the inference of multiple change-points in locally stationary time series. In contrast to traditional change-point analysis where an abrupt change occurs in a real-valued parameter, a change in locally stationary time series occurs in a parameter curve, and can be classified as a jump or a kink depending on whether the curve is discontinuous or not. We show that the proposed method can consistently estimate the number, locations, and the types of change-points. Two different asymptotic distributions corresponding respectively to jump and kink estimators are also established. Extensive simulation studies and a real data application to financial time series are provided.

翻译：变点检测与局部平稳时间序列建模是分析非平稳数据的两种主要方法。前者旨在通过检测时间序列模型动态特性中的突变来识别平稳阶段，而后者则采用（局部）时变模型来描述时间序列依赖结构的平滑变化。然而，在某些应用中，突变与平滑变化可能同时存在，此时单独使用任一种方法均无法充分建模数据。本文提出一种基于似然的新方法，用于推断局部平稳时间序列中的多重变点。与传统变点分析中实值参数发生突变不同，局部平稳时间序列中的变点发生在参数曲线上，并可根据曲线是否连续分为跳跃型与转折型。我们证明所提方法能够一致地估计变点的数量、位置与类型。同时建立了分别对应于跳跃型与转折型估计量的两种不同渐近分布。研究提供了广泛的模拟分析及对金融时间序列的实际数据应用。