Long-Range Dependence and Self-Similarity

Real-world time series rarely satisfy simple assumptions, often exhibiting long-range dependence. Ignoring this undermines accurate detection of trends and other important behavior. This text for graduate students and researchers in statistics and probability is also a reference for specialists in fields such as economics, finance, and hydrology.

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.