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.

翻译：现实世界系统中的变点标志着系统动态性的显著体制转变，这些转变可能由外生或内生因素触发。这些点界定了系统时间演化的体制，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。基于\cite{c:07}中引入的贝叶斯方法，我们设计了一种用于单变量时间序列均值在线变点检测的新方法，该方法非常适合实时应用，并且能够处理许多实证背景下数据所展现的一般时间模式。首先，我们将时间序列描述为任意阶的自回归过程。其次，允许数据的方差和相关性在每个体制内变化，这是通过一个评分规则驱动的，该规则更新参数值以更好地拟合观测数据。最后，通过当前体制长度的后验分布，在概率框架中检测变点。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精度和预测能力。使用各种数据集进行的实证验证表明，该方法在捕捉记忆和动态模式方面具有有效性，为现实世界系统的非平稳动态性提供了更深入的见解。