This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for identifying change-points in the mean of data coming from such a model, aiming to detect shifts in the underlying distribution. Additionally, we propose a consistent estimator for the spectral density of the data, contingent upon fundamental assumptions, notably the long-run variance. By leveraging probabilistic techniques, our approach provides reliable tools for understanding temporal changes in linear process data. Through theoretical analysis and empirical evaluation, we demonstrate the efficacy and consistency of our proposed methods, offering valuable insights for practitioners in various fields dealing with time series data analysis. Finally, we implemented our method on bitcoin data for identifying the time points of significant changes in its stock price.

翻译：本研究深入探讨了一种用于分析具有弱相关新息线性过程数据的概率方法，重点在于检测均值变点并估计其谱密度。我们开发了一种检验方法，用于识别来自此类模型数据的均值变点，旨在检测底层分布的偏移。此外，我们提出了一种在满足基本假设（特别是长期方差）条件下数据谱密度的一致性估计量。通过运用概率技术，我们的方法为理解线性过程数据的时序变化提供了可靠工具。通过理论分析和实证评估，我们证明了所提方法的有效性与一致性，为处理时间序列数据分析的各领域从业者提供了有价值的见解。最后，我们将该方法应用于比特币数据，以识别其股价发生显著变化的时间点。