Theory and Applications of Long-Range Dependence

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Paul Doukhan, George Oppenheim, Murad Taqqu
Springer Science & Business Media, Dec 13, 2002 - Mathematics - 720 pages

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.

 

 

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Contents

Historical Comments Related to Fractional Brownian Motion
39
Models Inequalities and Limit Theorems for Stationary Sequences
43
Limit Theorems under Seasonal LongMemory
101
Diagram Formula with Illustrations
111
UStatistics Multinomial Formula and Approximations of Multiple ItoWiener Integrals
129
A Decomposition for Generalized UStatistics of LongMemory Linear Processes
143
Limit Theorems for Infinite Variance Sequences
157
Fractional Calculus and Its Connections to Fractional Brownian Motion
165
Applications
369
Applications
371
LongRange Dependence and Data Network Traffic
373
Large Deviations of Queues with LongRange Dependent Input
409
The LongRange Dependence Paradigm for Macroeconomics and Finance
417
Thomas Mikosch
439
LongRange Dependence in Hydrology
461
Wavelet Based Estimation of Local Kolmogorov Turbulence
473

Stochastic Integration with Respect to Fractional Brownian Motion
203
Statistics
227
Parametric Estimation Under LongRange Dependence
229
Semiparametric Spectral Estimation for Fractional Processes
251
Nonparametric Estimation for LongRange Dependent Sequences
303
Estimation of Long Memory in Volatility
313
Detection and Estimation of Changes in Regime
325
Robust Estimators in Regression Models with Long Memory Errors
339
Prediction of LongMemory Time Series
355
Limit Theorems for the Burgers Equation Initialized by Data with LongRange Dependence
507
Methodology
525
SelfSimilarity and LongRange Dependence through the Wavelet Lens
527
A Survey
557
A Survey
579
Multifractal Processes
625
List of Authors
717
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