Online Change-Point Detection in Linear Regression with Autoregressive Errors via Streaming Variational Bayes

Abstract

Large-scale streaming time-series regression requires methods that can detect structural changes while accounting for serially correlated errors and quantifying uncertainty about the current regime. We propose a streaming variational Bayes method for linear regression with autoregressive errors that combines online changepoint detection with sequential posterior inference. The proposed method processes observations in chronological mini-batches and uses a finite-mixture variational approximation to represent separate retention and reset configurations for the regression coefficients and innovation variance, while the autoregressive coefficients are shared across regimes and learned sequentially. This construction yields block-specific changepoint probabilities and posterior uncertainty summaries. Closed-form variational updates and mixture pruning enable scalable sequential inference without repeated full-data refits. In simulations, the proposed method maintains low empirical false-alarm rates under stable regimes, with posterior coverage improving as the sample size increases. Under repeated structural changes, it provides accurate type-specific changepoint detection, small changepoint location errors, and short detection delays relative to frequentist sequential monitoring procedures, while posterior coverage approaches nominal levels after an initial adaptation period. An application to high-frequency Bitcoin volatility data illustrates distinct adaptation of the regression and innovation-variance components while accounting for residual autoregressive dependence.