SINGULAR SPECTRUM ANALYSIS FOR TIME SERIES

Preface to the Second Edition
Contents
1 Introduction
	1.1 Overview of SSA Methodology and the Structure of the Book
	1.2 SSA-Related Topics Outside the Scope of This Book
	1.3 SSA and Other Techniques
		1.3.1 Origins of SSA and Similar Techniques
		1.3.2 Is SSA a Linear Method?
		1.3.3 SSA and Autoregression
		1.3.4 SSA and Linear Regression for Trend Estimation
		1.3.5 SSA and DFT, EMD, DWT
		1.3.6 SSA and Signal Detection; Monte Carlo SSA
	1.4 Computer Implementation of SSA
	1.5 Historical and Bibliographical Remarks
	1.6 Common Symbols and Acronyms
	References
2 Basic SSA
	2.1 The Main Algorithm
		2.1.1 Description of the Algorithm
		2.1.2 Analysis of the Four Steps in Basic SSA
	2.2 Potential of Basic SSA
		2.2.1 Extraction of Trends and Smoothing
		2.2.2 Extraction of Periodic Components
		2.2.3 Complex Trends and Periodicities with Varying Amplitudes
		2.2.4 Finding Structure in Short Time Series
		2.2.5 Envelopes of Oscillating Signals and Estimation of Volatility
	2.3 Models of Time Series and SSA Objectives
		2.3.1 SSA and Models of Time Series
		2.3.2 Classification of the Main SSA Tasks
		2.3.3 Separability of Components of Time Series
	2.4 Choice of Parameters in Basic SSA
		2.4.1 General Issues
		2.4.2 Grouping for Given Window Length
		2.4.3 Window Length
		2.4.4 Signal Extraction
		2.4.5 Automatic Identification of SSA Components
	2.5 Some Variations of Basic SSA
		2.5.1 Preprocessing
		2.5.2 Prior and Posterior Information in SSA
		2.5.3 Rotations for Separability
		2.5.4 Sequential SSA
		2.5.5 SSA and Outliers
		2.5.6 Replacing the SVD with Other Procedures
		2.5.7 Complex SSA
	2.6 Multidimensional and Multivariate Extensions of SSA
		2.6.1 MSSA
		2.6.2 2D-SSA
		2.6.3 Shaped SSA
	References
3 SSA for Forecasting, Interpolation, Filtering and Estimation
	3.1 SSA Forecasting Algorithms
		3.1.1 Main Ideas and Notation
		3.1.2 Formal Description of the Algorithms
		3.1.3 SSA Forecasting Algorithms: Similarities and Dissimilarities
		3.1.4 Appendix: Vectors in a Subspace
	3.2 LRR and Associated Characteristic Polynomials
		3.2.1 Roots of the Characteristic Polynomials
		3.2.2 Min-Norm LRR
	3.3 Recurrent Forecasting as Approximate Continuation
		3.3.1 Approximate Separability and Forecasting Errors
		3.3.2 Approximate Continuation and Characteristic Polynomials
	3.4 Confidence Bounds for the Forecasts
		3.4.1 Monte Carlo and Bootstrap Confidence Intervals
		3.4.2 Confidence Intervals: Comparison of Forecasting Methods
	3.5 Summary and Recommendations on Forecasting Parameters
	3.6 Case Study: `Fortified Wine'
	3.7 Imputation of Missing Values
	3.8 Subspace-Based Methods and Estimation of Signal Parameters
		3.8.1 Basic Facts
		3.8.2 ESPRIT
		3.8.3 Overview of Other Subspace-Based Methods
		3.8.4 Hankel SLRA
	3.9 SSA and Filters
		3.9.1 Linear Filters and Their Characteristics
		3.9.2 SSA Reconstruction as a Linear Filter
		3.9.3 Middle Point Filter
		3.9.4 Last Point Filter and Forecasting
		3.9.5 Causal SSA (Last-Point SSA)
	3.10 Multidimensional/Multivariate SSA
		3.10.1 MSSA
		3.10.2 2D-SSA
	References