Overview
- Offers mathematically oriented statisticians tools for studying non-linear time-series
- Discusses moment based techniques
- Richly illustrated with examples and simulations
- Provides material for mathematicians entering the field of non-linear time series
Part of the book series: Mathématiques et Applications (MATHAPPLIC, volume 80)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (13 chapters)
-
Front Matter
-
Independence and Stationarity
-
Front Matter
-
-
Models of Time Series
-
Front Matter
-
-
Dependence
-
Front Matter
-
-
Back Matter
Keywords
- 60G10 37M10 32A25 60F05 60F15 60G18
- 60G12 60J05 62J12 62M10 62M15 91B84
- Non-linear time series
- Integer valued models
- Markov chains
- Stochastic processes
- Gaussian convergence
- Spectral estimation
- Memory models
- LARCH-type models
- Weak dependence conditions
- Functional estimation
- Bootstrap
- Non-Markove linear models
About this book
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series.
Reviews
“We are dealing with a monograph that compiles a broad set of fundamental results on the probabilistic and statistical analysis of time series, and is mathematically rigorous and effectively suitable to support theoretical and practical re-search in the general field of stochastic processes.” (Nazare Mendes Lopes, Mathematical Reviews, July, 2019)
“Although there are several books written on time series and stochastic processes, this book is the first one to present stochastic modelling approaches in linear/nonlinear time series. … This book is intended for masters and higher undergraduate students in mathematics, probability, statistics, astrophysics, biomedical engineering, and neuroscience. However, the students who want to pursue a PhD in the modelling of non-linear time series should also read this book to gain fundamental background knowledge.” (Chitaranjan Mahapatra, ISCB News, iscb.info, Issue 67, June, 2019)
“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.” (Nikolai N. Leonenko, zbMATH 1401.62007, 2019)
Authors and Affiliations
About the author
Paul Doukhan is a Professor at the University of Cergy-Pontoise, Paris. He is an established researcher in the area of non-linear time series. Chiefly focusing on the dependence of stochastic processes, he has published a large number of methodological research papers and authored several books in this research area.
Bibliographic Information
Book Title: Stochastic Models for Time Series
Authors: Paul Doukhan
Series Title: Mathématiques et Applications
DOI: https://doi.org/10.1007/978-3-319-76938-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-76937-0Published: 25 May 2018
eBook ISBN: 978-3-319-76938-7Published: 17 April 2018
Series ISSN: 1154-483X
Series E-ISSN: 2198-3275
Edition Number: 1
Number of Pages: XX, 308
Number of Illustrations: 19 b/w illustrations, 10 illustrations in colour
Topics: Statistical Theory and Methods, Probability Theory and Stochastic Processes, Econometrics, Dynamical Systems and Ergodic Theory