🤖 AI Summary
This work addresses the limitations of existing online change-point detection methods, which typically assume independent and identically distributed (i.i.d.) data and thus struggle with real-world time series exhibiting autocorrelation, often resulting in high false alarm rates or detection delays. To overcome this, the authors extend the generalized likelihood ratio (GLR) test to p-th order autoregressive (AR(p)) processes and integrate it with an enhanced FOCUS algorithm, yielding a computationally efficient online detector termed AR(p)-FOCUS. This approach is the first to explicitly model temporal dependencies within the GLR framework, achieving significantly improved detection performance while maintaining an average per-iteration computational complexity of O(log n). Empirical evaluations demonstrate that AR(p)-FOCUS outperforms conventional i.i.d.-based methods on autocorrelated data and exhibits strong effectiveness and practicality on real-world telecommunications datasets.
📝 Abstract
Changepoint detection methods have seen considerable development in recent years, with online algorithms capable of identifying structural changes in streaming data in near real time. However, the majority of existing methods are designed under the assumption of IID observations, rendering them susceptible to either more false positives or longer detection delays when applied to data exhibiting temporal dependence, a common feature of many real-world data streams. In this article, we extend the generalised likelihood-ratio (GLR) statistic to autoregressive processes of order $p$, and adapt the focus algorithm to develop a computationally efficient online change detector. The resulting AR($p$)-focus algorithm achieves an average computational cost of $\mathcal{O}(\log n)$ per iteration, making it suitable for high-frequency data streams. Through simulation studies, the proposed approach is seen achieving greater detection power than IID-based tests when the underlying data exhibit temporal correlation. We further illustrate the practical utility of AR($p$)-focus through an application to a real-world telecommunications dataset.