×

Stochastic models for time series. (English) Zbl 1401.62007

Mathématiques & Applications (Berlin) 80. Cham: Springer (ISBN 978-3-319-76937-0/pbk; 978-3-319-76938-7/ebook). xx, 308 p. (2018).
This book deals with different aspects of linear and nonlinear time series analysis. The book is divided into 12 chapters. The purpose of Chapters 1–4 is to introduce some underlying framework and machinery to form a base for the development of stochastic models for time series. Chapter 5 focuses on Gaussian chaos. Chapter 6 deals with linear processes. Chapter 7 focuses on nonlinear processes (Volterra expansions, Appell polynomials, bilinear models, ARCH-type models). Chapter 8 deals with associated processes (mathematical inequalities and limit theorems). Chapter 9 deals with dependence and ergodic theorems. The long-range dependence and related problems are discussed in Chapter 10, while short-range dependence and related limit theorems are given in Chapter 11. Chapter 12 deals with moments, cumulants and related inequalities.
The book is well written and mathematically rigorous. The author is certainly one of the best specialists in the field worldwide. He has collected a large variety of results. To date there is no book like this. It may become the standard reference for researchers working on the topic.
In summary, this is a very useful book for a researcher in probability and stochastic processes, which can also be used for under- and post-graduate courses.

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes
37M10 Time series analysis of dynamical systems
62M15 Inference from stochastic processes and spectral analysis
62M20 Inference from stochastic processes and prediction
62M05 Markov processes: estimation; hidden Markov models
PDFBibTeX XMLCite
Full Text: DOI