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

TL;DR

This paper introduces a Bayesian autoregressive method for online change-point detection in univariate time series, capable of handling time-varying parameters and complex temporal patterns, suitable for real-time applications.

Contribution

It develops a novel Bayesian approach that models autoregressive processes with dynamic variance and correlation, improving detection accuracy and adaptability over existing methods.

Findings

Effective in capturing non-stationary dynamics

Improves change point detection accuracy

Enhances forecasting power

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.