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集中于检测整个时间序列内的变点（离线方法），或对顺序观测数据中的变点进行最快检测（在线方法）。这两类方法均关注已发生的变点。而关于未来变点可能何时发生这一更为重要的问题，目前仍很大程度上未被探索。本文提出了一种描述变点发生机制的新颖统计模型。具体而言，该模型假设一个以非负创新驱动的随机游走形式的潜在过程，以及一个当潜在过程处于不同状态时表现不同的观测过程。通过模型构造，变点的发生等价于潜在过程触及状态阈值。因此，通过预测潜在过程何时将触及下一个状态阈值，即可对未来变点进行预测。本文建立了模型的概率性质，如平稳性和遍历性。提出了一种基于复合似然的方法用于参数估计和模型选择。此外，基于估计模型构建了未来变点的预测器及预测区间。