This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally.
Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.
Table of Contents
I Retrospective Problems
1 Preliminary considerations
2 General Retrospective Disorder Problem
3 Retrospective Detection and Estimation of Stochastic Trends
4 Retrospective Detection and Estimation of Switches in Univariate Models
5 Retrospective change-point detection and estimation in multivariate stochastic models
6 Retrospective Detection of Change-Points in State-Space Models
7 Copula, GARCH, and Other Financial Models
II Sequential Problems
8 Sequential hypothesis testing
9 Sequential change-point detection for univariate models
10 Sequential Change-Point Detection in Multivariate Models
11 Early change-point detection
12 Sequential Detection of Switches in Models with Changing Structures
13 Sequential detection and estimation of change-points
"The objective of this book is to present theoretical and numerical results for detection and estimation of changes in complex systems. Retrospective and sequential detection of the change-points is considered. …
I think that the book will be useful to many people because it presents the two types of change-point problems (retrospective and sequential), in various situations, presenting the theoretical results, simulations and real-world applications."
—Gabriela Ciuperca, in Mathematical Reviews Clippings, December 2017