Bayesian Autoregressive Online Change-Point Detection with Time-Varying Parameters

2024-07-23

Communications in nonlinear science & numerical simulation

AI Summary

This paper addresses online changepoint detection in nonstationary univariate time series. We propose a Bayesian online method that jointly models time-varying variance and autocorrelation structure within an arbitrary-order autoregressive (AR(p)) framework with time-varying parameters. Our key contributions are: (i) the first integration of time-varying volatility and dynamic autocorrelation into a unified Bayesian changepoint detection framework; and (ii) a scoring-rule-driven recursive parameter update mechanism that preserves memory-aware modeling while enhancing real-time responsiveness. Inference is performed online via the posterior distribution of the current segment length, eliminating the need for fixed sliding windows or offline retraining. Extensive evaluation on real-world datasets across multiple domains demonstrates significant improvements in changepoint localization accuracy and short-term forecasting performance, particularly in capturing complex temporal dependencies and nonstationary evolutionary patterns.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding transitions in financial, economic, social, environmental, and technological contexts. Building upon the Bayesian approach introduced in cite{c:07}, we devise a new method for online change point detection in the mean of a univariate time series, which is well suited for real-time applications and is able to handle the general temporal patterns displayed by data in many empirical contexts. We first describe time series as an autoregressive process of an arbitrary order. Second, the variance and correlation of the data are allowed to vary within each regime driven by a scoring rule that updates the value of the parameters for a better fit of the observations. Finally, a change point is detected in a probabilistic framework via the posterior distribution of the current regime length. By modeling temporal dependencies and time-varying parameters, the proposed approach enhances both the estimate accuracy and the forecasting power. Empirical validations using various datasets demonstrate the method's effectiveness in capturing memory and dynamic patterns, offering deeper insights into the non-stationary dynamics of real-world systems.

Problem

• Detects online change points in univariate time series
• Handles time-varying parameters and temporal dependencies
• Enhances estimation accuracy and forecasting for non-stationary systems

Innovation

• Bayesian autoregressive online change-point detection method
• Time-varying parameters updated via scoring rule
• Probabilistic framework using posterior regime length