Singular Spectrum Analysis with R (Use R!)

Singular Spectrum Analysis with R (Use R!)

Nina Golyandina
Anton Korobeynikov
Anatoly Zhigljavsky

Springer, 2018 (see companion site with examples)

Description

This book has the following goals:

  • to present the up-to-date SSA methodology, including multidimensional extensions, in the form accessible to a very wide circle of users,
  • to interconnect a variety of versions of SSA into a single tool,
  • to show the diverse tasks that SSA can be used for
  • to formally describe the main SSA methods and algorithms, and
  • to make a tutorial on the "Rssa" package.

Contents

1.           Introduction: Overview

1.1.       General Scheme of the SSA family and the main concepts

1.1.1.    SSA methods

1.1.2.    The main concepts

1.2.       Different versions of SSA

1.2.1.    Decomposition of X into a sum of rank-one matrices

1.2.2.    Versions of SSA dealing with different forms of the object

1.3.       Separability in SSA

1.4.       Forecasting, interpolation, low-rank approximation and parameter estimation in SSA

1.5.       The package

1.5.1.    SSA packages

1.5.2.    Tools for visual control and choice of parameters

1.5.3.    Short introduction to Rssa

1.5.4.    Implementation efficiency

1.6.       Comparison of SSA with other methods.

1.6.1.    Fourier transform, filtering, noise reduction

1.6.2.    Parametric regression

1.6.3.    ARIMA and ETS

1.7.       Bibliographical notes

1.7.1.    Short history

1.7.2.    Some recent applications of SSA

1.7.3.    SSA for preprocessing / combination of methods

1.7.4.    Materials used in this book

1.8.       Installation of Rssa and description of the data used in the book

1.8.1.    Installation of Rssa and usage comments

1.8.2.    Data description

2.           SSA analysis of one-dimensional time series

2.1.       Basic SSA

2.1.1.    Method

2.1.2.    Appropriate time series

2.1.3.    Separability and choice of parameters

2.1.4.    Algorithm

2.1.5.    Basic SSA in Rssa

2.2.       Toeplitz SSA

2.2.1.    Method

2.2.2.    Algorithm

2.2.3.    Toeplitz SSA in Rssa

2.3.       SSA with projection

2.3.1.    Method

2.3.2.    Appropriate time series

2.3.3.    Separability

2.3.4.    Algorithm

2.3.5.    SSA with projection in Rssa

2.4.       Iterative Oblique SSA

2.4.1.    Method

2.4.2.    Separability

2.4.3.    Algorithms

2.4.4.    Iterative O-SSA in Rssa

2.5.       Filter-adjusted O-SSA and SSA with derivatives

2.5.1.    Method

2.5.2.    Separability

2.5.3.    Algorithm

2.5.4.    Filter-adjusted O-SSA in Rssa

2.6.       Shaped 1D-SSA

2.6.1.    Method

2.6.2.    Separability

2.6.3.    Algorithm

2.6.4.    Shaped SSA in Rssa

2.7.       Automatic grouping in SSA

2.7.1.    Methods

2.7.2.    Algorithm

2.7.3.    Automatic grouping in Rssa

2.8.       Case studies

2.8.1.    Extraction of trend and oscillations by frequency ranges

2.8.2.    Trends in short series

2.8.3.    Trend and seasonality of complex form

2.8.4.    Finding noise envelope

2.8.5.    Elimination of edge effects

2.8.6.    Extraction of linear trends

2.8.7.    Automatic decomposition

2.8.8.    Log-transformation

3.           Parameter estimation, forecasting, gap filling

3.1.       Parameter estimation

3.1.1.    Method

3.1.2.    Algorithms

3.1.3.    Estimation in Rssa

3.2.       Forecasting

3.2.1.    Method

3.2.2.    Algorithms

3.2.3.    Forecasting in Rssa

3.3.       Gap filling

3.3.1.    Method

3.3.2.    Algorithms

3.3.3.    Gap-filling in Rssa

3.4.       Structured low-rank approximation

3.4.1.    Cadzow iterations

3.4.2.    Algorithms

3.4.3.    Structured low-rank approximation in Rssa

3.5.       Case studies

3.5.1.    Forecasting of complex trend and seasonality

3.5.2.    Different methods of forecasting

3.5.3.    Choice of parameters and confidence intervals

3.5.4.    Gap filling

3.5.5.    Parameter estimation and low-rank approximation

3.5.6.    Subspace tracking

3.5.7.    Automatic choice of parameters for forecasting

3.5.8.    Comparison of SSA, ARIMA, and ETS

4.           SSA for multivariate time series

4.1.       Complex SSA

4.1.1.    Method

4.1.2.    Separability

4.1.3.    Algorithm

4.1.4.    Complex SSA in Rssa

4.2.       MSSA analysis

4.2.1.    Method

4.2.2.    Multi-dimensional time series and LRRs

4.2.3.    Separability

4.2.4.    Comments on 1D-SSA, MSSA and Complex SSA

4.2.5.    Algorithm

4.2.6.    MSSA analysis in Rssa

4.3.       MSSA forecasting

4.3.1.    Method

4.3.2.    Algorithms

4.3.3.    MSSA forecasting in Rssa

4.3.4.    Other subspace-based MSSA extensions

4.4.       Case studies

4.4.1.    Analysis of series in different scales (normalization)

4.4.2.    Forecasting of series with different lengths and filling-in

4.4.3.    Simultaneous decomposition of many series

5.           Image processing

5.1.       2D-SSA

5.1.1.    Method

5.1.2.    Elements of 2D-SSA theory

5.1.3.    Algorithm

5.1.4.    2D-SSA in Rssa

5.2.       Shaped 2D-SSA

5.2.1.    Method

5.2.2.    Rank of shaped arrays

5.2.3.    Algorithm

5.2.4.    Shaped 2D-SSA in Rssa

5.2.5.    Comments on nD extensions

5.3.       2D ESPRIT

5.3.1.    Method

5.3.2.    Theory: Conditions of the algorithm correctness

5.3.3.    Algorithm

5.3.4.    2D-ESPRIT in Rssa

5.4.       Case studies

5.4.1.    Extraction of texture from non-rectangle images

5.4.2.    Adaptive smoothing

5.4.3.    Analysis of data given on a cylinder

5.4.4.    Analysis of nD objects: decomposition of a color image

 

Companion site contains a lot of useful information ubcluding the R code of all examples from the book with results of their run.

You can buy the book on Amazon.com or on the Springer site.

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