Singular Spectrum Analysis

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Singular Spectrum Analysis for Time Series

Nina Golyandina,Anatoly Zhigljavsky
Singular Spectrum Analysis for Time Series Book PDF

Author : Nina Golyandina,Anatoly Zhigljavsky
Publisher : Springer Science & Business Media
Page : 126 pages
File Size : 50,6 Mb
Release : 2013-01-19
Category : Mathematics
ISBN : 9783642349133

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Singular Spectrum Analysis for Time Series by Nina Golyandina,Anatoly Zhigljavsky Pdf

Singular spectrum analysis (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 seeks to decompose the original series into a sum of a small number of interpretable components such as trend, oscillatory components and noise. It is based on the singular value decomposition of a specific matrix constructed upon the time series. Neither a parametric model nor stationarity are assumed for the time series. This makes SSA a model-free method and hence enables SSA to have a very wide range of applicability. The present book is devoted to the methodology of SSA and shows how to use SSA both safely and with maximum effect. Potential readers of the book include: professional statisticians and econometricians, specialists in any discipline in which problems of time series analysis and forecasting occur, specialists in signal processing and those needed to extract signals from noisy data, and students taking courses on applied time series analysis.

Singular Spectrum Analysis

J.B. Elsner,A.A. Tsonis
Singular Spectrum Analysis Book PDF

Author : J.B. Elsner,A.A. Tsonis
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 54,5 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9781475725148

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Singular Spectrum Analysis by J.B. Elsner,A.A. Tsonis Pdf

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.

Singular Spectrum Analysis with R

Nina Golyandina,Anton Korobeynikov,Anatoly Zhigljavsky
Singular Spectrum Analysis with R Book PDF

Author : Nina Golyandina,Anton Korobeynikov,Anatoly Zhigljavsky
Publisher : Springer
Page : 272 pages
File Size : 47,8 Mb
Release : 2018-06-14
Category : Mathematics
ISBN : 9783662573808

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Singular Spectrum Analysis with R by Nina Golyandina,Anton Korobeynikov,Anatoly Zhigljavsky Pdf

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.

Singular Spectrum Analysis of Biomedical Signals

Saeid Sanei,Hossein Hassani
Singular Spectrum Analysis of Biomedical Signals Book PDF

Author : Saeid Sanei,Hossein Hassani
Publisher : CRC Press
Page : 260 pages
File Size : 42,6 Mb
Release : 2015-12-23
Category : Medical
ISBN : 9781466589285

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Singular Spectrum Analysis of Biomedical Signals by Saeid Sanei,Hossein Hassani Pdf

Recent advancements in signal processing and computerised methods are expected to underpin the future progress of biomedical research and technology, particularly in measuring and assessing signals and images from the human body. This book focuses on singular spectrum analysis (SSA), an effective approach for single channel signal analysis, and its bivariate, multivariate, tensor based, complex-valued, quaternion-valued and robust variants. SSA currently has numerous applications in detecting abnormalities in quasi-periodic biosignals, such as electrocardiograms, (ECGs or EKGs), oxygen levels, arterial pressure, and electroencephalograms (EEGs). Singular Spectrum Analysis of Biomedical Signals presents relatively newly applied concepts for biomedical applications of SSA, including: Signal source separation, extraction, decomposition, and factorization Physiological, biological, and biochemical signal processing A new SSA grouping algorithm for filtering and noise reduction of genetics data Prediction of various clinical events The book introduces a new mathematical and signal processing technique for the decomposition of widely available single channel biomedical data. It also provides illustrations of new signal processing results in the form of signals, graphs, images, and tables to reinforce understanding of the related concepts. Singular Spectrum Analysis of Biomedical Signals enhances current clinical knowledge and aids physicians in improving diagnosis, treatment and monitoring some clinical abnormalities. It also lays groundwork for progress in SSA by making suggestions for future research.

Singular Spectrum Analysis for Time Series

Nina Golyandina,Anatoly Zhigljavsky
Singular Spectrum Analysis for Time Series Book PDF

Author : Nina Golyandina,Anatoly Zhigljavsky
Publisher : Springer Nature
Page : 156 pages
File Size : 41,8 Mb
Release : 2020-11-23
Category : Mathematics
ISBN : 9783662624364

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Singular Spectrum Analysis for Time Series by Nina Golyandina,Anatoly Zhigljavsky Pdf

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.

Analysis of Time Series Structure

Nina Golyandina,Vladimir Nekrutkin,Anatoly A Zhigljavsky
Analysis of Time Series Structure Book PDF

Author : Nina Golyandina,Vladimir Nekrutkin,Anatoly A Zhigljavsky
Publisher : CRC Press
Page : 322 pages
File Size : 43,7 Mb
Release : 2001-01-23
Category : Mathematics
ISBN : 1420035843

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Analysis of Time Series Structure by Nina Golyandina,Vladimir Nekrutkin,Anatoly A Zhigljavsky Pdf

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.

Singular Spectrum Analysis

Hossein Hassani,Rahim Mahmoudvand
Singular Spectrum Analysis Book PDF

Author : Hossein Hassani,Rahim Mahmoudvand
Publisher : Springer
Page : 158 pages
File Size : 46,9 Mb
Release : 2018-06-25
Category : Business & Economics
ISBN : 9781137409515

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Singular Spectrum Analysis by Hossein Hassani,Rahim Mahmoudvand Pdf

This book provides a broad introduction to computational aspects of Singular Spectrum Analysis (SSA) which is a non-parametric technique and requires no prior assumptions such as stationarity, normality or linearity of the series. This book is unique as it not only details the theoretical aspects underlying SSA, but also provides a comprehensive guide enabling the user to apply the theory in practice using the R software. Further, it provides the user with step- by- step coding and guidance for the practical application of the SSA technique to analyze their time series databases using R. The first two chapters present basic notions of univariate and multivariate SSA and their implementations in R environment. The next chapters discuss the applications of SSA to change point detection, missing-data imputation, smoothing and filtering. This book is appropriate for researchers, upper level students (masters level and beyond) and practitioners wishing to revive their knowledge of times series analysis or to quickly learn about the main mechanisms of SSA.

Modern Singular Spectral-Based Denoising and Filtering Techniques for 2D and 3D Reflection Seismic Data

R. K. Tiwari,R. Rekapalli
Modern Singular Spectral Based Denoising and Filtering Techniques for 2D and 3D Reflection Seismic Data Book PDF

Author : R. K. Tiwari,R. Rekapalli
Publisher : Springer Nature
Page : 165 pages
File Size : 41,8 Mb
Release : 2020-03-25
Category : Science
ISBN : 9783030193041

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Modern Singular Spectral-Based Denoising and Filtering Techniques for 2D and 3D Reflection Seismic Data by R. K. Tiwari,R. Rekapalli Pdf

This book discusses the latest advances in singular spectrum-based algorithms for seismic data processing, providing an update on recent developments in this field. Over the past few decades, researchers have extensively studied the application of the singular spectrum-based time and frequency domain eigen image methods, singular spectrum analysis (SSA) and multichannel SSA for various geophysical data. This book addresses seismic reflection signals, which represent the amalgamated signals of several unwanted signals/noises, such as ground roll, diffractions etc. Decomposition of such non-stationary and erratic field data is one of the multifaceted tasks in seismic data processing. This volume also includes comprehensive methodological and parametric descriptions, testing on appropriately generated synthetic data, as well as comparisons between time and frequency domain algorithms and their applications to the field data on 1D, 2D, 3D and 4D data sets. Lastly, it features an exclusive chapter with MATLAB coding for SSA.

Time-Series Analysis and Cyclostratigraphy

Graham P. Weedon
Time Series Analysis and Cyclostratigraphy Book PDF

Author : Graham P. Weedon
Publisher : Cambridge University Press
Page : 275 pages
File Size : 42,5 Mb
Release : 2005-09-15
Category : Science
ISBN : 9781139435178

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Time-Series Analysis and Cyclostratigraphy by Graham P. Weedon Pdf

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.

Modelling and Simulation of Complex Systems for Sustainable Energy Efficiency

Ahmed Hammami,Philippus Stephanus Heyns,Stephan Schmidt,Fakher Chaari,Mohamed Slim Abbes,Mohamed Haddar
Modelling and Simulation of Complex Systems for Sustainable Energy Efficiency Book PDF

Author : Ahmed Hammami,Philippus Stephanus Heyns,Stephan Schmidt,Fakher Chaari,Mohamed Slim Abbes,Mohamed Haddar
Publisher : Springer Nature
Page : 270 pages
File Size : 40,6 Mb
Release : 2021-08-21
Category : Technology & Engineering
ISBN : 9783030855840

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Modelling and Simulation of Complex Systems for Sustainable Energy Efficiency by Ahmed Hammami,Philippus Stephanus Heyns,Stephan Schmidt,Fakher Chaari,Mohamed Slim Abbes,Mohamed Haddar Pdf

This book provides readers with an overview of recent theories and methods for studying complex mechanical systems used in energy production, such as wind turbines, but not limited to them. The emphasis is put on strategies for increasing energy efficiency, and on recent industrial applications. Topics cover dynamics and vibration, vibroacoustics, engineering design, modelling and simulation, fault diagnostics, signal processing and prognostics. The book is based on peer-review contributions and invited talks presented at the first International Workshop on MOdelling and Simulation of COmplex Systems for Sustainable Energy Efficiency, MOSCOSSEE 2021, held online on February 25-26, 2021, and organized by the LAboratory of Mechanics, Modelling and Production (LA2MP) from University of Sfax, Tunisia and the Department of Mechanical and Aeronautical engineering, Centre of Asset Integrity Management (C-AIM) from University of Pretoria, South Africa. By offering authoritative information on innovative methods and tools for application in renewable energy production, it provides a valuable resource to both academics and professionals, and a bridge to facilitate communication between the two groups.

Digital Signal Processing and Spectral Analysis for Scientists

Silvia Maria Alessio
Digital Signal Processing and Spectral Analysis for Scientists Book PDF

Author : Silvia Maria Alessio
Publisher : Springer
Page : 900 pages
File Size : 43,8 Mb
Release : 2015-12-09
Category : Technology & Engineering
ISBN : 9783319254685

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Digital Signal Processing and Spectral Analysis for Scientists by Silvia Maria Alessio Pdf

This book covers the basics of processing and spectral analysis of monovariate discrete-time signals. The approach is practical, the aim being to acquaint the reader with the indications for and drawbacks of the various methods and to highlight possible misuses. The book is rich in original ideas, visualized in new and illuminating ways, and is structured so that parts can be skipped without loss of continuity. Many examples are included, based on synthetic data and real measurements from the fields of physics, biology, medicine, macroeconomics etc., and a complete set of MATLAB exercises requiring no previous experience of programming is provided. Prior advanced mathematical skills are not needed in order to understand the contents: a good command of basic mathematical analysis is sufficient. Where more advanced mathematical tools are necessary, they are included in an Appendix and presented in an easy-to-follow way. With this book, digital signal processing leaves the domain of engineering to address the needs of scientists and scholars in traditionally less quantitative disciplines, now facing increasing amounts of data.

Spectral Algorithms

Ravindran Kannan,Santosh Vempala
Spectral Algorithms Book PDF

Author : Ravindran Kannan,Santosh Vempala
Publisher : Now Publishers Inc
Page : 153 pages
File Size : 48,8 Mb
Release : 2009
Category : Computers
ISBN : 9781601982742

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Spectral Algorithms by Ravindran Kannan,Santosh Vempala Pdf

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Stochastic Global Optimization

Anatoly Zhigljavsky,Antanasz Zilinskas
Stochastic Global Optimization Book PDF

Author : Anatoly Zhigljavsky,Antanasz Zilinskas
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 44,9 Mb
Release : 2007-11-20
Category : Mathematics
ISBN : 9780387747408

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Stochastic Global Optimization by Anatoly Zhigljavsky,Antanasz Zilinskas Pdf

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.

Geophysical Signal Analysis

Enders A. Robinson,Sven Treitel
Geophysical Signal Analysis Book PDF

Author : Enders A. Robinson,Sven Treitel
Publisher : SEG Books
Page : 481 pages
File Size : 54,9 Mb
Release : 2000
Category : Digital filters (Mathematics).
ISBN : 9781560801047

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Geophysical Signal Analysis by Enders A. Robinson,Sven Treitel Pdf

Addresses the construction, analysis, and interpretation of mathematical and statistical models. The practical use of the concepts and techniques developed is illustrated by numerous applications. The chosen examples will interest many readers, including those engaged in digital signal analysis in disciplines other than geophysics.

Automatic Autocorrelation and Spectral Analysis

Piet M. T. Broersen
Automatic Autocorrelation and Spectral Analysis Book PDF

Author : Piet M. T. Broersen
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 42,8 Mb
Release : 2006-04-20
Category : Computers
ISBN : 9781846283284

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Automatic Autocorrelation and Spectral Analysis by Piet M. T. Broersen Pdf

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.