Analysis of Time Series Structure: SSA and Related Techniques

Analysis of Time Series Structure

SSA and Related Techniques

Nina Golyandina
Vladimir Nekrutkin
Anatoly Zhigljavsky



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.


Part I.   SSA: Methodology13
1Basic SSA15
 1.1    Basic SSA: description16
 1.2    Steps in Basic SSA: comments18
 1.3    Basic SSA: basic capabilities24
 1.4    Time series and SSA tasks32
 1.5    Separability44
 1.6    Choice of SSA parameters53
 1.7    Supplementary SSA techniques78
2SSA forecasting93
 2.1    SSA recurrent forecasting algorithm95
 2.2    Continuation and approximate continuation96
 2.3    Modifications to Basic SSA R-forecasting107
 2.4    Forecast confidence bounds115
 2.5    Summary and recommendations127
 2.6    Examples and effects131
3SSA detection of structural changes149
 3.1    Main definitions and concepts149
 3.2    Homogeneity and heterogeneity156
 3.3    Heterogeneity and separability169
 3.4    Choice of detection parameters189
 3.5    Additional detection characteristics196
 3.6    Examples204
Part II.   SSA: Theory217
4Singular value decomposition219
 4.1    Existence and uniqueness219
 4.2    SVD matrices222
 4.3    Optimality of SVDs227
 4.4    Centring in SVD232
5Time series of finite rank237
 5.1    General properties237
 5.2    Series of finite rank and recurrent formulae243
 5.3    Time series continuation252
6SVD of trajectory matrices257
 6.1    Mathematics of separability257
 6.2    Hankelization266
 6.3    Centring in SSA268
 6.4    SSA for stationary series276
List of Data Sets and Their Sources297

You can buy the book on or on the CRC Press site.

You can download all the real-life data used in the book's examples here.

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