DETECTING CHANGE-POINTS IN THE MEAN OF MULTIVARIATE TIME SERIES

Abstract

After providing a detailed literature review of the change-point detection methods, this work delves into presenting a probabilistic method for analyzing linear process data with 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 the data, 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.