Singular Spectrum Analysis
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Singular Spectrum Analysis
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Author : J.B. Elsner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Singular Spectrum Analysis written by J.B. Elsner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Business & Economics categories.
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
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Author : Hossein Hassani
language : en
Publisher: Springer
Release Date : 2018-06-25
Singular Spectrum Analysis written by Hossein Hassani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-25 with Business & Economics categories.
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.
Singular Spectrum Analysis For Time Series
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Author : Nina Golyandina
language : en
Publisher: Springer Nature
Release Date : 2020-11-23
Singular Spectrum Analysis For Time Series written by Nina Golyandina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Mathematics categories.
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.
Singular Spectrum Analysis With R
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Author : Nina Golyandina
language : en
Publisher: Springer
Release Date : 2018-06-14
Singular Spectrum Analysis With R written by Nina Golyandina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-14 with Mathematics categories.
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
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Author : Saeid Sanei
language : en
Publisher: CRC Press
Release Date : 2015-12-23
Singular Spectrum Analysis Of Biomedical Signals written by Saeid Sanei and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-23 with Medical categories.
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
Singular Spectrum Analysis
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Author : No Kang Myung
language : en
Publisher:
Release Date : 2009
Singular Spectrum Analysis written by No Kang Myung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Theoretical Advancements And Applications In Singular Spectrum Analysis
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Author : Agampodige Emmanuel Diyanath Sirimal Silva
language : en
Publisher:
Release Date : 2016
Theoretical Advancements And Applications In Singular Spectrum Analysis written by Agampodige Emmanuel Diyanath Sirimal Silva and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Multivariate And 2d Extensions Of Singular Spectrum Analysis With The Rssa Package
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Author : Nina Golyandina
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2015-02-08
Multivariate And 2d Extensions Of Singular Spectrum Analysis With The Rssa Package written by Nina Golyandina and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-08 with categories.
Implementation of multivariate and 2D extensions of singular spectrum analysis (SSA) by means of the R-package Rssa is considered. The extensions include MSSA for simultaneous analysis and forecasting of several time series and 2D-SSA for analysis of digital images. A new extension of 2D-SSA analysis called Shaped 2D-SSA is introduced for analysis of images of arbitrary shape, not necessary rectangular. It is shown that implementation of Shaped 2D-SSA can serve as a base for implementation of MSSA and other generalizations. Efficient implementation of operations with Hankel and Hankel-block-Hankel matrices through the fast Fourier transform is suggested. Examples with code fragments in R, which explain the methodology and demonstrate the proper use of Rssa, are presented.
Some Statistical Aspects Of Singular Spectrum Analysis
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Author : Md. Atikur Rahman Khan
language : en
Publisher:
Release Date : 2013
Some Statistical Aspects Of Singular Spectrum Analysis written by Md. Atikur Rahman Khan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Singular spectrum analysis (SSA) is a nonparametric technique that has gained popularity to decompose the observed series into the sum of orthogonal and interpretable components. SSA is akin to the classical decomposition of a time series into the sum of trend, cyclical, seasonal and noise components. Reconstruction of signal is a critical initial step in SSA that underlies any application, such as forecasting, or the analysis of missing data or change point detection problems. Two basic parameters: the window length of the embedding, and the dimension of the signal that must be assigned by the practitioner, are very important for optimal reconstruction of signal. A set of statistical tests and an information theoretic criterion for optimal reconstruction of signal have been proposed in this thesis.The standard approach of selecting a very large window length is to ensure the orthogonality of the components by comparing the image plot of the weighted correlation matrix for different window lengths. Apart from such pattern evaluation and the hurdle of finding a window length that provides a clear view of the image plot, we propose a new methodology for selectingthe window length in SSA in which the window length is determined from the data prior to the commencement of modeling. This selection procedure is based on statistical tests designed to test the convergence of the autocovariance function for both short- and long-memory processes. Asymptotic properties of these test statistics are found to be consistent with simulation results. Furthermore, application to Southern Oscillation Index data shows how this approach can enhance the reconstruction and predictive performance of SSA.Information theoretic analysis of the signal-noise separation problem in SSA is also provided in this thesis. A minimum description length criterion is proposed based on the signal-plus-noise model obtained through the Karhunen-Loeve expansion of the trajectory matrix. Under very general regularity conditions the criterion is found to identify the true signal dimension with probability of one as the sample size increases. Furthermore, empirical results from simulationexperiments and real data analysis indicate that even in the case of relatively small samples the asymptotic theory is reflected in observed behavior.Assessment of the quality of separation and reconstruction of signal is carried out by introducing two measures: mean squared separation error (MSSE) and mean squared reconstruction error (MSRE). Algebraic and asymptotic bounds for both MSSE and MSRE are then used to assess the quality of signal extracted by employing an SSA. While the former is implementable only when thetrue signal is known, the latter is implementable for any observed process and this behavior is reflected in both simulation results and real data analysis.Mean squared forecast error (MSFE) is a measure of checking forecast accuracy of a time series model, and theoretical results of MSFE based on the linear recurrence relation are established through the eigen-decomposition of the trajectory matrix. Two extreme classes of processes, AR(1) and RW processes, are considered in this thesis to assess the window length effect on MSFE. While the objectively defined window length selection by evaluating MSRE is deemed favorable for an AR(1) process, the smallest possible window length supports the RW forecasting of a series. Theoretical results are also reflected in simulation experiments and real data analysis.
The Singular Spectrum Analysis Method And Its Application To Seismic Data Denoising And Reconstruction
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Author : Vicente E. Oropeza
language : en
Publisher:
Release Date : 2010
The Singular Spectrum Analysis Method And Its Application To Seismic Data Denoising And Reconstruction written by Vicente E. Oropeza and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Seismology categories.