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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
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