Change-point detection and estimation procedures have been widely developed in the literature. However, commonly used approaches in change-point analysis have mainly been focusing on detecting change-points within an entire time series (off-line methods), or quickest detection of change-points in sequentially observed data (on-line methods). Both classes of methods are concerned with change-points that have already occurred. The arguably more important question of when future change-points may occur, remains largely unexplored. In this paper, we develop a novel statistical model that describes the mechanism of change-point occurrence. Specifically, the model assumes a latent process in the form of a random walk driven by non-negative innovations, and an observed process which behaves differently when the latent process belongs to different regimes. By construction, an occurrence of a change-point is equivalent to hitting a regime threshold by the latent process. Therefore, by predicting when the latent process will hit the next regime threshold, future change-points can be forecasted. The probabilistic properties of the model such as stationarity and ergodicity are established. A composite likelihood-based approach is developed for parameter estimation and model selection. Moreover, we construct the predictor and prediction interval for future change points based on the estimated model.

翻译：变点检测与估计方法已在文献中得到广泛发展。然而，变点分析中常用的方法主要关注识别整个时间序列中的变点（离线方法），或在序贯观测数据中最快速检测变点（在线方法）。这两类方法均针对已发生的变点。而一个更具重要性的问题——未来变点可能何时出现——仍未被充分探索。本文提出了一种描述变点发生机制的新型统计模型。具体而言，该模型假设潜变量过程为受非负新息驱动的随机游走，而观测过程在潜变量过程处于不同区域时呈现不同行为。根据模型构造，变点的发生等价于潜变量过程触及区域阈值。因此，通过预测潜变量过程何时触及下一个区域阈值，可实现对未来变点的预报。本文建立了模型的概率性质（如平稳性和遍历性），开发了基于复合似然的参数估计与模型选择方法，并基于估计模型构建了未来变点的预测值与预测区间。