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Author: Nina Golyandina
Publisher: Springer Nature
ISBN: 3662624362
Category : Mathematics
Languages : en
Pages : 156
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Book Description
This book gives an overview of singular spectrum analysis (SSA). SSA is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas. Rapidly increasing number of novel applications of SSA is a consequence of the new fundamental research on SSA and the recent progress in computing and software engineering which made it possible to use SSA for very complicated tasks that were unthinkable twenty years ago. In this book, the methodology of SSA is concisely but at the same time comprehensively explained by two prominent statisticians with huge experience in SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The second edition of the book contains many updates and some new material including a thorough discussion on the place of SSA among other methods and new sections on multivariate and multidimensional extensions of SSA.
Author: Nina Golyandina
Publisher: Springer Nature
ISBN: 3662624362
Category : Mathematics
Languages : en
Pages : 156
Get Book Here
Book Description
This book gives an overview of singular spectrum analysis (SSA). SSA is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas. Rapidly increasing number of novel applications of SSA is a consequence of the new fundamental research on SSA and the recent progress in computing and software engineering which made it possible to use SSA for very complicated tasks that were unthinkable twenty years ago. In this book, the methodology of SSA is concisely but at the same time comprehensively explained by two prominent statisticians with huge experience in SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The second edition of the book contains many updates and some new material including a thorough discussion on the place of SSA among other methods and new sections on multivariate and multidimensional extensions of SSA.
Author: J.B. Elsner
Publisher: Springer Science & Business Media
ISBN: 1475725140
Category : Business & Economics
Languages : en
Pages : 167
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Book Description
The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make the matrix A -AI singular. The term singular spectrum analysis· is unfortunate since the traditional eigenvalue decomposition involving multivariate data is also an analysis of the singular spectrum. More properly, singular spectrum analysis (SSA) should be called the analysis of time series using the singular spectrum. Spectral decomposition of matrices is fundamental to much the ory of linear algebra and it has many applications to problems in the natural and related sciences. Its widespread use as a tool for time series analysis is fairly recent, however, emerging to a large extent from applications of dynamical systems theory (sometimes called chaos theory). SSA was introduced into chaos theory by Fraedrich (1986) and Broomhead and King (l986a). Prior to this, SSA was used in biological oceanography by Colebrook (1978). In the digi tal signal processing community, the approach is also known as the Karhunen-Loeve (K-L) expansion (Pike et aI., 1984). Like other techniques based on spectral decomposition, SSA is attractive in that it holds a promise for a reduction in the dimen- • Singular spectrum analysis is sometimes called singular systems analysis or singular spectrum approach. vii viii Preface sionality. This reduction in dimensionality is often accompanied by a simpler explanation of the underlying physics.
Author: Nina Golyandina
Publisher: Springer
ISBN: 3662573806
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This comprehensive and richly illustrated volume provides up-to-date material on Singular Spectrum Analysis (SSA). SSA is a well-known methodology for the analysis and forecasting of time series. Since quite recently, SSA is also being used to analyze digital images and other objects that are not necessarily of planar or rectangular form and may contain gaps. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas, most notably those associated with time series and digital images. An effective, comfortable and accessible implementation of SSA is provided by the R-package Rssa, which is available from CRAN and reviewed in this book. Written by prominent statisticians who have extensive experience with SSA, the book (a) presents the up-to-date SSA methodology, including multidimensional extensions, in language accessible to a large circle of users, (b) combines different versions of SSA into a single tool, (c) shows the diverse tasks that SSA can be used for, (d) formally describes the main SSA methods and algorithms, and (e) provides tutorials on the Rssa package and the use of SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The book is written on a level accessible to a broad audience and includes a wealth of examples; hence it can also be used as a textbook for undergraduate and postgraduate courses on time series analysis and signal processing.
Author: Nina Golyandina
Publisher: CRC Press
ISBN: 9781420035841
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing. However, despite the promise it holds for time series applications in other disciplines, SSA is not widely known among statisticians and econometrists, and although the basic SSA algorithm looks simple, understanding what it does and where its pitfalls lay is by no means simple. Analysis of Time Series Structure: SSA and Related Techniques provides a careful, lucid description of its general theory and methodology. Part I introduces the basic concepts, and sets forth the main findings and results, then presents a detailed treatment of the methodology. After introducing the basic SSA algorithm, the authors explore forecasting and apply SSA ideas to change-point detection algorithms. Part II is devoted to the theory of SSA. Here the authors formulate and prove the statements of Part I. They address the singular value decomposition (SVD) of real matrices, time series of finite rank, and SVD of trajectory matrices. Based on the authors' original work and filled with applications illustrated with real data sets, this book offers an outstanding opportunity to obtain a working knowledge of why, when, and how SSA works. It builds a strong foundation for successfully using the technique in applications ranging from mathematics and nonlinear physics to economics, biology, oceanology, social science, engineering, financial econometrics, and market research.
Author: Graham P. Weedon
Publisher: Cambridge University Press
ISBN: 1139435175
Category : Science
Languages : en
Pages : 275
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Book Description
Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and tidal cycles. It is suitable for senior undergraduate and graduate courses in environmental science, palaeoceanography and geology.
Author: Anatoly Zhigljavsky
Publisher: Springer Science & Business Media
ISBN: 0387747400
Category : Mathematics
Languages : en
Pages : 269
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Book Description
This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.
Author: Vadim Olshevsky
Publisher: World Scientific
ISBN: 9814469556
Category : Mathematics
Languages : en
Pages : 604
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Book Description
Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.
Author: Carla Braitenberg
Publisher: Springer
ISBN: 3319962779
Category : Science
Languages : en
Pages : 323
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Book Description
This volume treats the key aspects that must be known when dealing with continuous space geodetic or terrestrial geodetic observations. The signals of Earth core resonance are discussed, as well as tidal effects on Earth polar motion and on earthquake triggering. Hydrologic loading, be it ocean tides or subsurface water flows, is discussed. These signals compete with crustal deformation observations of earthquakes (e.g., Gorkha 2015) during interseismic periods, and on volcanoes (Elbrus, Caucasus). The instrumentation that is covered includes superconducting gravimeters, continuous seafloor gravimeters, interferometric tilt and strain meters, and GNSS networks. The articles give an up-to-date account of research in which the Earth tides are a benchmark signal for the sophisticated instrumentation mounted on satellites or the surface, observing time-variable signals of an evolving Earth. Scientists studying the earthquake cycle and geodetic monitoring will find useful material. For students in the geosciences, the collection offers a good overview of the broad spectrum of topics related to the Earth geodetic monitoring.
Author: G. Larry Bretthorst
Publisher: Springer Science & Business Media
ISBN: 146849399X
Category : Mathematics
Languages : en
Pages : 210
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Book Description
This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docu ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared.
Author: Piet M. T. Broersen
Publisher: Springer Science & Business Media
ISBN: 1846283280
Category : Computers
Languages : en
Pages : 301
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Book Description
Spectral analysis requires subjective decisions which influence the final estimate and mean that different analysts can obtain different results from the same stationary stochastic observations. Statistical signal processing can overcome this difficulty, producing a unique solution for any set of observations but that is only acceptable if it is close to the best attainable accuracy for most types of stationary data. This book describes a method which fulfils the above near-optimal-solution criterion, taking advantage of greater computing power and robust algorithms to produce enough candidate models to be sure of providing a suitable candidate for given data.
