Singular Spectrum Analysis for Time Series

Nina Golyandina received her MSc and PhD degrees in mathematics at St.Petersburg State University, Russia, in 1985 and 1998, respectively. She started to work at St.Petersburg State University in 1985, where she is currently an Associate Professor of Statistical Modelling Department, Faculty of Mathematics and Mechanics. Her main areas of research interest are statistical modeling and applied statistics, especially time series investigation by means of singular spectrum analysis. Dr. Golyandina is the coauthor of three monographs on singular spectrum analysis and of more than 30 research papers in refereed journals related to applied probability and statistics. During last twenty years, she was involved in different projects related to singular spectrum analysis. Anatoly Zhigljavsky has received his BSc, MSc and PhD degrees in mathematics and statistics at Faculty of Mathematics, St.Petersburg State University. He became professor of statistics at the St.Petersburg State University in 1989. Since 1997 he is a professor, Chair in Statistics at Cardiff University. Anatoly Zhigljavsky is the author or co-author of 10 monographs on the topics of time series analysis, stochastic global optimization, optimal experimental design and dynamical systems; he is the editor/co-editor of 9 books on various topics and the author of more than 150 research papers in refereed journals. He has organized several major conferences on time series analysis, experimental design and global optimization. In 2019, he has received a prestigious Constantine Caratheodory award by the International Society for Global Optimization for his contribution to stochastic optimization.

1 Introduction.- 1.1 Overview of SSA methodology and the structure of the book.- 1.2 SSA and other techniques.- 1.3 Computer implementation of SSA.- 1.4 Historical and bibliographical remarks.- 1.5 Common symbols and acronyms.- 2 Basic SSA - 2.1 The main algorithm.- 2.2 Potential of Basic SSA.- 2.3 Models of time series and SSA objectives.- 2.4 Choice of parameters in Basic SSA.- 2.5 Some variations of Basic SSA.- 2.6 Multidimensional and multivariate extensions of SSA.- 3 SSA for forecasting, interpolation, filtering and estimation.- 3.1 SSA forecasting algorithms.- 3.2 LRR and associated characteristic polynomials.- 3.3 Recurrent forecasting as approximate continuation.- 3.4 Confidence bounds for the forecasts.- 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.- 3.9 SSA and filters.- 3.10 Multidimensional/Multivariate SSA.