Analysis of Time Series Structure: SSA and Related Techniques

Analysis of Time Series Structure

SSA and Related Techniques

Nina Golyandina
Vladimir Nekrutkin
Anatoly Zhigljavsky

CHAPMAN & HALL/CRC, 2001

Description

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.


Preface		ix
Notation		xi
Introduction		1
Part I. SSA: Methodology		13
1	Basic SSA	15
	1.1 Basic SSA: description	16
	1.2 Steps in Basic SSA: comments	18
	1.3 Basic SSA: basic capabilities	24
	1.4 Time series and SSA tasks	32
	1.5 Separability	44
	1.6 Choice of SSA parameters	53
	1.7 Supplementary SSA techniques	78
2	SSA forecasting	93
	2.1 SSA recurrent forecasting algorithm	95
	2.2 Continuation and approximate continuation	96
	2.3 Modifications to Basic SSA R-forecasting	107
	2.4 Forecast confidence bounds	115
	2.5 Summary and recommendations	127
	2.6 Examples and effects	131
3	SSA detection of structural changes	149
	3.1 Main definitions and concepts	149
	3.2 Homogeneity and heterogeneity	156
	3.3 Heterogeneity and separability	169
	3.4 Choice of detection parameters	189
	3.5 Additional detection characteristics	196
	3.6 Examples	204
Part II. SSA: Theory		217
4	Singular value decomposition	219
	4.1 Existence and uniqueness	219
	4.2 SVD matrices	222
	4.3 Optimality of SVDs	227
	4.4 Centring in SVD	232
5	Time series of finite rank	237
	5.1 General properties	237
	5.2 Series of finite rank and recurrent formulae	243
	5.3 Time series continuation	252
6	SVD of trajectory matrices	257
	6.1 Mathematics of separability	257
	6.2 Hankelization	266
	6.3 Centring in SSA	268
	6.4 SSA for stationary series	276
List of Data Sets and Their Sources		297
References		299
Index		303

You can buy the book on Amazon.com 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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