This paper addresses the problem of detecting change points in the spectral density of time series, motivated by EEG analysis of seizure patients. Seizures disrupt coherence and functional connectivity, necessitating precise detection. Departing from traditional parametric approaches, we utilize the Wold decomposition, representing general time series as autoregressive processes with infinite lags, which are truncated and estimated around the change point. Our detection procedure employs an initial estimator that systematically searches across time points. We examine the localization error and its dependence on time series properties and sample size. To enhance accuracy, we introduce an optimal rate method with an asymptotic distribution, facilitating the construction of confidence intervals. The proposed method effectively identifies seizure onset in EEG data and extends to event detection in video data. Comprehensive numerical experiments demonstrate its superior performance compared to existing techniques.

翻译：本文针对癫痫患者脑电图分析中的需求，研究时间序列谱密度变点检测问题。癫痫发作会破坏神经信号的相干性与功能连接性，因此需要精确检测变点。与传统参数化方法不同，我们采用沃尔德分解，将一般时间序列表示为无限滞后自回归过程，并在变点附近进行截断与估计。检测程序采用一种在时间点上系统搜索的初始估计量。我们分析了定位误差及其对时间序列特性与样本量的依赖关系。为提高精度，我们提出具有渐近分布的最优速率方法，以构建置信区间。该方法能有效识别脑电图数据中的癫痫发作起始点，并可扩展至视频数据的事件检测。综合数值实验表明，其性能优于现有技术。