AI 中文总结
研究在数据存在自相关时的在线变点检测问题，将广义似然比统计量扩展到p阶自回归过程，结合聚焦算法开发出AR（p）-聚焦算法，该算法计算高效，适用于高频数据流，检测能力优于基于IID的检验。
AI 中文摘要
近年来，变点检测方法有了显著发展，在线算法能够近乎实时地识别流数据中的结构变化。然而，大多数现有方法是在独立同分布（IID）观测假设下设计的，当应用于具有时间依赖性的数据时，它们容易出现更多误报或更长的检测延迟，而时间依赖性是许多现实世界数据流的常见特征。在本文中，我们将广义似然比（GLR）统计量扩展到p阶自回归过程，并采用聚焦算法开发了一种计算高效的在线变化检测器。由此产生的AR（p）-聚焦算法每次迭代的平均计算成本为\(\mathcal{O}(\log n)\)，适用于高频数据流。通过模拟研究，当基础数据表现出时间相关性时，所提出的方法比基于IID的检验具有更高的检测能力。我们还通过将AR（p）-聚焦应用于一个现实世界的电信数据集来说明其实用性。
英文摘要
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.
