The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject. The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques." Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature. The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text. The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject.   The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques."   Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature.   The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text.   Preface vii Part A: Theory 1(2) Probability 3(224) Fractional Brownian Motion and Long-Range Dependence 5(34) Murad S. Taqqu Historical Comments Related to Fractional Brownian Motion 39(4) George M. Molchan Models, Inequalities, and Limit Theorems for Stationary Sequences 43(58) Paul Doukhan Limit Theorems under Seasonal Long-Memory 101(10) Mohamedou Ould Haye Marie-Claude Viano CLTs for Polynomials of Linear Sequences: Diagram Formula with Illustrations 111(18) D. Surgailis Non-CLTs: U-Statistics, Multinomial Formula and Approximations of Multiple Ito-Wiener Integrals 129(14) D. Surgailis A Decomposition for Generalized U-Statistics of Long-Memory Linear Processes 143(14) Hwai-Chung Ho Tailen Hsing Limit Theorems for Infinite Variance Sequences 157(8) Makoto Maejima Fractional Calculus and Its Connections to Fractional Brownian Motion 165(38) Vladas Pipiras Murad S. Taqqu Stochastic Integration with Respect to Fractional Brownian Motion 203(24) Laurent Decreusefond Statistics 227(142) Parametric Estimation Under Long-Range Dependence 229(22) L. Giraitis P. M. Robinson Semiparametric Spectral Estimation for Fractional Processes 251(52) Eric Moulines Philippe Soulier Nonparametric Estimation for Long-Range Dependent Sequences 303(10) Paul Doukhan Abdelali Khezour Gabriel Lang Estimation of Long Memory in Volatility 313(12) Rohit S. Deo Clifford M. Hurvich Detection and Estimation of Changes in Regime 325(14) Piotr Kokoszka Remigijus Leipus Robust Estimators in Regression Models with Long Memory Errors 339(16) H. L. Koul D. Surgailis Prediction of Long-Memory Time Series 355(14) R. J. Bhansali P. S. Kokoszka Part B: Applications 369(2) Applications 371(154) Long-Range Dependence and Data Network Traffic 373(36) Walter Willinger Vern Paxson Rolf H. Riedi Murad S. Taqqu Large Deviations of Queues with Long-Range Dependent Input 409(8) Ilkka Norros The Long-Range Dependence Paradigm for Macroeconomics and Finance 417(22) Marc Henry Paolo Zaffaroni Long-Range Dependence Effects and ARCH Modeling 439(22) Thomas Mikosch Catalin Starica Long-Range Dependence in Hydrology 461(12) Alberto Montanari Wavelet Based Estimation of Local Kolmogorov Turbulence 473(34) George C. Papanicolaou Knut Sølna Limit Theorems for the Burgers Equation Initialized by Data with Long-Range Dependence 507(18) D. Surgailis W. A. Woyczynski Methodology 525(192) Self-Similarity and Long-Range Dependence through the Wavelet Lens 527(30) Patrice Abry Patrick Flandrin Murad S. Taqqu Darryl Veitch Semi-Parametric Estimation of the Long-Range Dependence Parameter: A Survey 557(22) Jean-Marc Bardet Gabriel Lang Georges Oppenheim Anne Philippe Stilian Stoev Murad S. Taqqu Generators of Long-Range Dependent Processes: A Survey 579(46) Jean-Marc Bardet Gabriel Lang Georges Oppenheim Anne Philippe Murad S. Taqqu Multifractal Processes 625(92) Rudolf H. Riedi List of Authors 717