Predicting Future Change-points in Time Series

TL;DR

This paper introduces a novel statistical model for forecasting future change-points in time series by modeling a latent process and predicting when it hits regime thresholds, addressing a largely unexplored problem.

Contribution

The paper develops a new probabilistic model and estimation method for predicting future change-points, extending beyond traditional detection to forecasting future occurrences.

Findings

Model assumptions ensure stationarity and ergodicity.

A composite likelihood approach effectively estimates model parameters.

The predictor provides accurate future change-point forecasts with confidence intervals.

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.