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Long-Memory Processes

Probabilistic Properties and Statistical Methods

  • Jan Beran
  • Yuanhua Feng
  • Sucharita Ghosh
  • Rafal Kulik

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 1-41
  3. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 43-106
  4. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 107-208
  5. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 209-384
  6. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 385-528
  7. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 529-554
  8. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 555-732
  9. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 733-752
  10. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 753-769
  11. Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik
    Pages 771-795
  12. Back Matter
    Pages 797-884

About this book

Introduction

Long-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.

Keywords

62Mxx, 62M09, 62M10, 60G18, 60G22, 60G52, 60G60, 91B84 asymptotic theory fractal processes long-memory processes statistical applications time series analysis/spatial processes/space-time processes

Authors and affiliations

  • Jan Beran
    • 1
  • Yuanhua Feng
    • 2
  • Sucharita Ghosh
    • 3
  • Rafal Kulik
    • 4
  1. 1.Dept. of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany
  2. 2.Faculty of Business, Administration and EconomicsUniversity of PaderbornPaderbornGermany
  3. 3.Swiss Federal Research Institute WSLBirmensdorfSwitzerland
  4. 4.Dept. of Mathematics and StatisticsUniversity of OttawaOttawaCanada

Bibliographic information

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