Predicting Future Change-points in Time Series

Chak Fung Choi; Chunxue Li; Chun Yip Yau; Zifeng Zhao

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arXiv · 2405.09485

Predicting Future Change-points in Time Series

Chak Fung Choi·Chunxue Li·Chun Yip Yau·Zifeng Zhao

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Abstract

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.

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BibTeX RIS

Chak Fung Choi, Chunxue Li, Chun Yip Yau, Zifeng Zhao. 2024-05-24. Predicting Future Change-points in Time Series. https://arxiv.org/abs/2405.09485

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