LONG-MEMORY PROCESSES: PROBABILISTIC PROPERTIES AND STATISTICAL METHODS

摘要

In the last 20 years or so, long-memory processes have become a subject of very intensive research in probability and statistics. The reason could be that the property of long memory is observed in many real time series from various fields such as geophysics, hydrology, telecommunications, economics, finance and climatology. Many classical limit theorems no longer are applicable in the case of long-memory stationary random processes. For instance, the square root laws of central limit theorems are not true anymore when the second-order spectrum of the stationary processes is not bounded; this causes several analytical difficulties in the derivation of analytic expressions and proofs associated with estimates obtained in the case of long-memory stationary processes. This book provides a comprehensive review of these, including a thorough discussion of mathematical and probabilistic foundations and statistical methods. The main focus is on processes with long memory, self-similar scaling or fractal properties and power laws. One can say that the book is too long, containing almost 900 pages. The list of chapters and sections is given subsequently.