Long-Range Dependence and Self-Similarity

A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.

Vladas Pipiras (Author), Murad S. Taqqu (Author)

9781107039469, Cambridge University Press

Hardback, published 18 April 2017

688 pages, 58 b/w illus. 8 tables
26 x 18.2 x 4.4 cm, 1.42 kg

'This is the most readable and lucid account I have seen on long-range dependence and self-similarity. Pipiras and Taqqu present a time-series-centric view of this subject that should appeal to both practitioners and researchers in stochastic processes and statistics. I was especially enamored by the insightful comments on the history of the subject that conclude each chapter. This alone is worth the price of the book!' Richard Davis, Columbia University, New York

This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.

List of abbreviations
Notation
Preface
1. A brief overview of times series and stochastic processes
2. Basics of long-range dependence and self-similarity
3. Physical models for long-range dependence and self-similarity
4. Hermite processes
5. Non-central and central limit theorems
6. Fractional calculus and integration of deterministic functions with respect to FBM
7. Stochastic integration with respect to fractional Brownian motion
8. Series representations of fractional Brownian motion
9. Multidimensional models
10. Maximum likelihood estimation methods
Appendix A. Auxiliary notions and results
Appendix B. Integrals with respect to random measures
Appendix C. Basics of Malliavin calculus
Appendix D. Other notes and topics
Bibliography
Index.

Subject Areas: Stochastics [PBWL], Probability & statistics [PBT], Econometrics [KCH]