Description
Book SynopsisLong-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.
Trade ReviewFrom the book reviews:
“This encyclopaedic book covers almost the whole literature on univariate and multivariate long-range dependent (LRD) processes, or long-memory processes or strongly dependent processes. … This volume is then of strong interest for both researchers and teachers familiar with the topic, as it gives an overall, structured and balanced picture of the current state of the art. Readers less familiar with the topic will easily find their way in the vast literature on this issue, and will have their curiosity satisfied.” (Gilles Teyssière, Mathematical Reviews, October, 2014)
“This book aims to cover probabilistic and statistical aspects of long-memory processes in as much detail as possible, including a broad range of topics. The authors did an excellent job to reach their goals, and the book would be a must for researchers interested in long-memory processes and practioners on time series and data analysis. … the book is an excellent choice for anyone who is working in fields related to long-memory processes with many update information and research topics.” (Weiping Li, zbMATH, Vol. 1282, 2014)
Table of ContentsDefinition of Long Memory.- Origins and Generation of Long Memory.- Mathematical Concepts.- Limit Theorems.- Statistical Inference for Stationary Processes.- Statistical Inference for Nonlinear Processes.- Statistical Inference for Nonstationary Processes.- Forecasting.- Spatial and Space-Time Processes.- Resampling.- Function Spaces.- Regularly Varying Functions.- Vague Convergence.- Some Useful Integrals.- Notation and Abbreviations.
