Long Range Dependence

Author : Paul Doukhan,George Oppenheim,Murad Taqqu
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 44,6 Mb
Release : 2002-12-13
Category : Mathematics
ISBN : 0817641688

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Theory and Applications of Long-Range Dependence by Paul Doukhan,George Oppenheim,Murad Taqqu Pdf

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.

Author : Gennady Samorodnitsky
Publisher : Springer
Page : 415 pages
File Size : 49,7 Mb
Release : 2016-11-09
Category : Mathematics
ISBN : 9783319455754

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Stochastic Processes and Long Range Dependence by Gennady Samorodnitsky Pdf

This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.

Author : Vladas Pipiras,Murad S. Taqqu
Publisher : Cambridge University Press
Page : 693 pages
File Size : 45,5 Mb
Release : 2017-04-18
Category : Business & Economics
ISBN : 9781107039469

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Long-Range Dependence and Self-Similarity by Vladas Pipiras,Murad S. Taqqu Pdf

A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.

Author : Gennady Samorodnitsky
Publisher : Now Publishers Inc
Page : 109 pages
File Size : 55,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9781601980908

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Long Range Dependence by Gennady Samorodnitsky Pdf

Long Range Dependence is a wide ranging survey of the ideas, models and techniques associated with the notion of long memory. It will serve as an invaluable reference source for researchers studying long range dependence, for those building long memory models, and for people who are trying to detect the possible presence of long memory in data.

Author : Jan Beran,Yuanhua Feng,Sucharita Ghosh,Rafal Kulik
Publisher : Springer Science & Business Media
Page : 892 pages
File Size : 50,9 Mb
Release : 2013-05-14
Category : Mathematics
ISBN : 9783642355127

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Long-Memory Processes by Jan Beran,Yuanhua Feng,Sucharita Ghosh,Rafal Kulik Pdf

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.

Author : Eberlein,Murad Taqqu
Publisher : Birkhäuser
Page : 496 pages
File Size : 53,6 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015017931968

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Dependence in Probability and Statistics by Eberlein,Murad Taqqu Pdf

Author : Paul Doukhan
Publisher : Springer
Page : 308 pages
File Size : 41,8 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319769387

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Stochastic Models for Time Series by Paul Doukhan Pdf

This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series.

Author : Jan Beran
Publisher : CRC Press
Page : 336 pages
File Size : 46,6 Mb
Release : 1994-10-01
Category : Mathematics
ISBN : 0412049015

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Statistics for Long-Memory Processes by Jan Beran Pdf

Statistical Methods for Long Term Memory Processes covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that previously appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasizes basic principles and practical applications and provides an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows readers to view statistical approaches in a practical context. Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the first three chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence.

Author : Ali Ercan,M. Levent Kavvas,Rovshan K. Abbasov
Publisher : Springer Science & Business Media
Page : 54 pages
File Size : 49,9 Mb
Release : 2013-08-30
Category : Mathematics
ISBN : 9783319015057

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Long-Range Dependence and Sea Level Forecasting by Ali Ercan,M. Levent Kavvas,Rovshan K. Abbasov Pdf

​This study shows that the Caspian Sea level time series possess long range dependence even after removing linear trends, based on analyses of the Hurst statistic, the sample autocorrelation functions, and the periodogram of the series. Forecasting performance of ARMA, ARIMA, ARFIMA and Trend Line-ARFIMA (TL-ARFIMA) combination models are investigated. The forecast confidence bands and the forecast updating methodology, provided for ARIMA models in the literature, are modified for the ARFIMA models. Sample autocorrelation functions are utilized to estimate the differencing lengths of the ARFIMA models. The confidence bands of the forecasts are estimated using the probability densities of the residuals without assuming a known distribution. There are no long-term sea level records for the region of Peninsular Malaysia and Malaysia’s Sabah-Sarawak northern region of Borneo Island. In such cases the Global Climate Model (GCM) projections for the 21st century can be downscaled to the Malaysia region by means of regression techniques, utilizing the short records of satellite altimeters in this region against the GCM projections during a mutual observation period. This book will be useful for engineers and researchers working in the areas of applied statistics, climate change, sea level change, time series analysis, applied earth sciences, and nonlinear dynamics.

Author : Jérome Dedecker,Paul Doukhan,Gabriel Lang,José Rafael Leon,Sana Louhichi,Clémentine Prieur
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 41,5 Mb
Release : 2007-07-29
Category : Mathematics
ISBN : 9780387699523

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Weak Dependence: With Examples and Applications by Jérome Dedecker,Paul Doukhan,Gabriel Lang,José Rafael Leon,Sana Louhichi,Clémentine Prieur Pdf

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.

Author : Jacques Lévy-Véhel,Evelyne Lutton
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 44,7 Mb
Release : 2005-12-06
Category : Technology & Engineering
ISBN : 9781846280481

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Fractals in Engineering by Jacques Lévy-Véhel,Evelyne Lutton Pdf

The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering field. The strong potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument, the qualitative observation of fractal phenomena no longer being sufficient. Consisting of papers written by a world-wide pool of experts, the multidisciplinary approach of this third volume will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds. Fractals in Engineering: New Trends in Theory and Applications continues the publication of engineering-related research in fractal techniques begun in Fractals in Engineering and Fractals: Theory and Applications in Engineering (Springer London 1997 and 1999).

Author : Ming Li,Carlo Cattani
Publisher : Frontiers Media SA
Page : 160 pages
File Size : 40,7 Mb
Release : 2022-12-05
Category : Science
ISBN : 9782832508503

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Long-Range Dependent Processes: Theory and Applications by Ming Li,Carlo Cattani Pdf

Author : S. N. Lahiri
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 49,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475738032

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Resampling Methods for Dependent Data by S. N. Lahiri Pdf

By giving a detailed account of bootstrap methods and their properties for dependent data, this book provides illustrative numerical examples throughout. The book fills a gap in the literature covering research on re-sampling methods for dependent data that has witnessed vigorous growth over the last two decades but remains scattered in various statistics and econometrics journals. It can be used as a graduate level text and also as a research monograph for statisticians and econometricians.

Author : P.M. Robinson,Murray Rosenblatt
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461224129

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Athens Conference on Applied Probability and Time Series Analysis by P.M. Robinson,Murray Rosenblatt Pdf

The Athens Conference on Applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes. Volume II presents papers on time series analysis, many of which were contributed to a meeting in March 1995 partly in honour of E.J. Hannan. The initial paper by P.M. Robinson discusses Ted Hannan's researches and their influence on current work in time series analysis. Other papers discuss methods for finite parameter Gaussian models, time series with infinite variance or stable marginal distribution, frequency domain methods, long range dependent processes, nonstationary processes, and nonlinear time series. The methods presented can be applied in a number of fields such as statistics, applied mathematics, engineering, economics and ecology. The papers include many of the topics of current interest in time series analysis and will be of interest to a wide range of researchers.

Author : George Agich
Publisher : Cambridge University Press
Page : 222 pages
File Size : 53,9 Mb
Release : 2003-08-07
Category : Family & Relationships
ISBN : 0521009200

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Dependence and Autonomy in Old Age by George Agich Pdf

Respecting the autonomy of disabled people is an important ethical issue for providers of long-term care. In this influential book, George Agich abandons comfortable abstractions to reveal the concrete threats to personal autonomy in this setting, where ethical conflict, dilemma and tragedy are inescapable. He argues that liberal accounts of autonomy and individual rights are insufficient, and offers an account of autonomy that matches the realities of long-term care. The book therefore offers a framework for carers to develop an ethic of long-term care within the complex environment in which many dependent and aged people find themselves. Previously published as Autonomy and Long-term Care, this revised edition, in paperback for the first time, takes account of recent work and develops the author's views of what autonomy means in the real world. It will have wide appeal among bioethicists and health care professionals.