# Analysis of Time Series Structure: SSA and Related Techniques

CRC Press, Jan 23, 2001 - Mathematics - 320 pages
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.

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### Contents

 Basic SSA 15 description 16 comments 18 basic capabilities 24 14 Time series and SSA tasks 32 15 Separability 44 16 Choice of SSA parameters 53 17 Supplementary SSA techniques 78
 35 Additional detection characteristics 196 36 Examples 204 SSA Theory 217 Singular value decomposition 219 42 SVD matrices 222 43 Optimality of SVDs 227 44 Centring in SVD 232 Time series of finite rank 237

 SSA forecasting 93 21 SSA recurrent forecasting algorithm 95 22 Continuation and approximate continuation 96 23 Modifications to Basic SSA Rforecasting 107 24 Forecast confidence bounds 115 25 Summary and recommendations 127 26 Examples and effects 131 SSA detection of structural changes 149 32 Homogeneity and heterogeneity 156 33 Heterogeneity and separability 169 34 Choice of detection parameters 189
 52 Series of finite rank and recurrent formulae 243 53 Time series continuation 252 SVD of trajectory matrices 257 62 Hankelization 266 63 Centring in SSA 268 64 SSA for stationary series 276 List of data sets and their sources 297 References 299 Index 303 Copyright

### References from web pages

statsnetbase: Statistical Sciences Online
Analysis of Time Series Structure: SSA and Related Techniques. Nina Golyandina Vladimir Nekrutkin Anatoly A Zhigljavsky ...
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Analysis of Time Series Structure: SSA and Related Techniques
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JSTOR: Analysis of Time Series Structure: SSA and Related Techniques
Analysis of Time Series Structure: SSA and Related Techniques. C. Chatfield. Biometrics, Vol. 57, No. 4, 1272-1273. Dec., 2001. ...

Journal of the American Statistical Association: Analysis of Time ...
Analysis of Time Series Structure: SSA and Related Techniques. (Book Reviews). James B. Elsner. Nina GOLYANDINA, Vladimir NEKRUTKIN, and Anatoly ZHIGLJAVSKY ...
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[1] Golyandina, N., V. Nekrutkin and A. Zhigljavsky (2001) Analysis of Time Series Structure: SSA and Related Techniques, Chapman & Hall/CRC. ...
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Robust Non-stationary Singular Spectrum Analysis of Chaotic Time ...
1. , av Kryanev. 1,2. , gv Lukin. 2. 1. Laboratory of Information Technologies, JINR. 2. Moscow Engineering Physics Institute, Moscow, RUSSIA. Abstract ...
lit.jinr.ru/ Reports/ annual-report05/ new-Report_of_Kryanev_2005-168.pdf

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Phys. Rev. E 72, 046710 (2005): Luo et al. - Optimal phase-space ...
N. Golyandina, V. Nekrutkin, and A. Zhigljavsky, Analysis of Time Series Structure: SSA and Related Techniques (Chapman and Hall/CRC, London, 2001). ...