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Analysis of Time Series Structure:

SSA and Related Techniques
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CRC Press, Dec 12, 2010 - 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

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Analysis of Time Series Structure: SSA and Related Techniques. C. Chatfield. Biometrics, Vol. 57, No. 4, 1272-1273. Dec., 2001. ...
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