Titlebook: Change Point Analysis for Time Series; Lajos Horváth,Gregory Rice Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusi

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0172-7397 modern settings of high--dimensional, functional, and heterThis volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of ch

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Cumulative Sum Processes,ved data. As such, we begin by developing a comprehensive asymptotic theory for CUSUM processes under conditions that allow for serial dependence in the observations. This includes a careful analysis of how weights applied to the CUSUM process affect the limiting distribution of its functionals, and extensions to multivariate observations.

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Regression Models,parametric regression model. In this case a change in the relationship may be characterized by a change in the model parameters. This chapter is devoted to the development of asymptotic methods to perform change point analysis in the context of regression models.

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Change Point Analysis of the Mean,points in the series, the functionals of the CUSUM process that we have considered should be consistent in the sense that they diverge in probability to positive infinity as the sample size grows. One goal of this chapter is to carefully quantify the asymptotic behaviour of the CUSUM process in the presence of change points.

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