Statistics for long-memory processes. (English) Zbl 0869.60045

Beran, Jan

Monographs on Statistics and Applied Probability. 61. London: Chapman & Hall. x, 315 p. (1994).

It is observed in diverse fields of statistical applications that correlation between observations that are far apart decay to zero at a slower rate than one would expect from independent data or data following classic ARMA- or Markov-type models. Therefore, long memory (or long-range dependence) has become a rapidly developing subject. Because of the diversity of applications, the literature on the topic is broadly scattered in a large number of journals, including those in fields such as agronomy, astronomy, chemistry, economics, engineering, environmental sciences, geosciences, hydrology, mathematics, physics and statistics. This is the first book to cover the diverse statistical methods and applications for data with long-range dependence.
The author provides a concise and accessible overview of probabilistic foundations, statistical methods and applications, with an emphasis on basic principles and practical applications, giving the reader an interesting perspective on theory and practice. He explores data set from a wide range of disciplines, with all data sets conveniently compiled in the appendix, enabling the reader to view statistical approaches in a practical context. He supplies a chapter with listing of some S-PLUS programs for the major methods discussed, allowing to apply long-memory processes in daily data analysis. For readers who are new to the area, the first three chapters give the basic knowledge required to read the rest of the book. Some elementary knowledge on time series analysis is helpful. For those familiar with the topic, the chapters can be read in arbitrary sequence. An extensive bibliography given at the end of the book should provide help for studying topics not covered here or not covered in detail.

Reviewer: J.C.Abril (Tucuman)

MSC:

60G99	Stochastic processes
60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60G18	Self-similar stochastic processes
60G10	Stationary stochastic processes

Keywords:

long-memory processes; self-similar processes; long-range dependence; statistical methods and applications for data with long-range dependence

Software:

S-PLUS; longmemo