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Particularities and commonalities of singular spectrum analysis as a method of time series analysis and signal processing

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Abstract Singular spectrum analysis (SSA), starting from the second half of the 20th century, has been a rapidly developing method of time series analysis. Since it can be called principal component analysis (PCA) for time series, SSA will definitely be a standard method in time series analysis and signal processing in the future. Moreover, the problems solved by SSA are considerably wider than that for PCA. In particular, the problems of frequency estimation, forecasting and missing values imputation can be solved within the framework of SSA. The idea of SSA came from different scientific communities, such as that of researchers in time series analysis (Karhunen–Loève decomposition), signal processing (low‐rank approximation and frequency estimation) and multivariate data analysis (PCA). Also, depending on the area of applications, different viewpoints on the same algorithms, choice of parameters, and methodology as a whole are considered. Thus, the aim of the paper is to describe and compare different viewpoints on SSA and its modifications and extensions to give people from different scientific communities the possibility to be aware of potentially new aspects of the method. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
“MotorVehicle,” monthly sales: decomposition
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“Tree rings”: periodograms of the reconstructed time series
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“Tree rings”: frequency decomposition
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“MotorVehicle” (5 years), DerivSSA with L = 24: trend reconstruction, ET9–11; good separability
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“MotorVehicle” (5 years), DerivSSA with L = 24: elementary reconstructed components; good separability
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“MotorVehicle” (5 years), singular spectrum analysis with L = 24: two trend reconstructions, ET1 and ET1–2; poor separability
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“MotorVehicle” (5 years), singular spectrum analysis with L = 24: elementary reconstructed components; poor separability
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“Fortified wines,” L = 84: decomposition for groups ET1, ET2–11, and ET12–84
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“Fortified wines,” L = 84: w‐correlations between elementary reconstructed components
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“Fortified wines,” L = 84: 2D scatterplots of eigenvectors (Ui(k), Ui+1(k)), k = 1, …, L
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“Fortified wines,” L = 84: one‐dimensional graphs of eigenvectors (k, Ui(k)), k = 1, …, L
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“Maya”: decomposition
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Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis

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