Analysis of Time Series Structure: SSA and Related TechniquesCRC Press, 23 հնվ, 2001 թ. - 320 էջ 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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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 |
299 | |
303 | |
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Common terms and phrases
A₁ amplitude amplitude-modulated analysis approximate separability assume asymptotic separability average triple Basic SSA bootstrap change-point characteristic polynomial coefficients column confidence intervals corresponding decomposition defined denote depicted in Fig described diagonal averaging Double centring eigentriple rearrangement eigenvalues eigenvectors equal example extraction Figure finite forecasting algorithm frequencies H-matrix Hankel Hankel matrix harmonic components harmonic series heterogeneity matrix homogeneous initial series inner product integer L-continuation L-lagged vectors leading eigentriples linear space min(L minimal LRF nonzero obtain original series orthogonal orthonormal P₁ parameters periodic periodogram problem Proposition reconstructed series recurrent continuation recurrent forecasting residual series row detection function Section sequence series components series F(1 series FN signal singular value decomposition singular values singular vectors span stationary series strong separability structure Theorem thick line thin line tion Toeplitz trajectory matrix trend U₁ vector forecasting weak separability white noise window length zero
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