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 Adams and MacKay (2007), 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.

中文翻译：

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具有时变参数的贝叶斯自回归在线变化点检测


现实世界系统中的变化点标志着系统动力学的重大制度转变，可能由外生或内生因素触发。这些点定义了系统时间演变的机制，对于理解金融、经济、社会、环境和技术背景下的转变至关重要。在 Adams 和 MacKay （2007） 中引入的贝叶斯方法的基础上，我们设计了一种以单变量时间序列为平均值的在线变化点检测新方法，该方法非常适合实时应用，并且能够处理数据在许多经验上下文中显示的一般时间模式。我们首先将时间序列描述为任意阶数的自回归过程。其次，允许数据的方差和相关性在由评分规则驱动的每个制度中变化，该评分规则更新参数的值以更好地拟合观测值。最后，通过当前制度长度的后验分布在概率框架中检测到一个变化点。通过对时间依赖性和时变参数进行建模，所提出的方法提高了估计的准确性和预测能力。使用各种数据集的实证验证证明了该方法在捕获内存和动态模式方面的有效性，从而提供了对现实世界系统的非平稳动力学的更深入见解。