Detecting Change-points in Mean of Multivariate Time Series

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.