LARGE SAMPLE INFERENCE FOR LONG MEMORY PROCESSES - Hardcover

Giraitis, Liudas; Koul, Hira L.; Surgailis, Donatas

Hardcover

ISBN 10: 1848162782 ISBN 13: 9781848162785

Publisher: Imperial College Press, 2011

Synopsis

A discrete-time stationary stochastic process with finite variance is said to have long memory if its autocorrelations tend to zero hyperbolically in the lag, i.e. like a power of the lag, as the lag tends to infinity. The absolute sum of autocorrelations of such processes diverges and their spectral density at the origin is unbounded. This is unlike the so-called weakly dependent processes, where autocorrelations tend to zero exponentially fast and the spectral density is bounded at the origin. In a long memory process, the dependence between the current observation and the one at a distant future is persistent; whereas in the weakly dependent processes, these observations are approximately independent. This fact alone is enough to warn a person about the validity of the classical inference procedures based on the square root of the sample size standardization when data are generated by a long-term memory process.The aim of this volume is to provide a text at the graduate level from which one can learn, in a concise fashion, some basic theory and techniques of proving limit theorems for numerous statistics based on long memory processes. It also provides a guide to researchers about some of the inference problems under long memory.

About this title

Review

"The book provides a systematic and unified rigorous discussion on the characteristics of the short and long memory processes and their applications in statistics. It is an excellent and useful book that I strongly recommend for theoretical researchers and practitioners who are interested in inference for long memory processes." -- Professor Linyuan Li, University of New Hampshire

Edition details

• Publisher: Imperial College Press
• Publication date: 2011
• Language: English
• ISBN 10: 1848162782
• ISBN 13: 9781848162785
• Binding: Hardcover
• Edition number: 1
• Number of pages: 577