Topic
Singular spectrum analysis
About: Singular spectrum analysis is a research topic. Over the lifetime, 1774 publications have been published within this topic receiving 51637 citations.
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Journal Article•
21 Mar 1991
TL;DR: In this article, the authors introduce the concept of Stationary Random Processes and Spectral Analysis in the Time Domain and Frequency Domain, and present an analysis of Processes with Mixed Spectra.
Abstract: Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the Time Domain. Estimation in the Frequency Domain. Spectral Analysis in Practice. Analysis of Processes with Mixed Spectra.
5,238 citations
Book•
01 Jan 2017
TL;DR: In this paper, simple descriptive techniques for time series estimation in the time domain forecasting stationary processes in the frequency domain spectral analysis bivariate processes linear systems state-space models and the Kalman filter non-linear models multivariate time series modelling some other topics.
Abstract: Simple descriptive techniques probability models for time series estimation in the time domain forecasting stationary processes in the frequency domain spectral analysis bivariate processes linear systems state-space models and the Kalman filter non-linear models multivariate time series modelling some other topics.
3,694 citations
TL;DR: The connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis are described.
Abstract: [1] The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.
2,116 citations
Book•
01 Jan 1990TL;DR: This work presents a meta-modelling framework for estimating the modeled properties of the Shannon filter, which automates the very labor-intensive and therefore time-heavy process of Fourier analysis.
Abstract: 1. Overview. 2. Fundamental Concepts. 3. Stationary Time Series Models. 4. Non-Stationary Time Series Models. 5. Forecasting. 6. Model Identification. 7. Parameter Estimation, Diagnostic Checking, and Model Selection. 8. Seasonal Time Series Models. 9. Intervention Analysis and Outlier Detection. 10. Fourier Analysis. 11. Spectral Theory of Stationary Processes. 12. Estimation of the Spectrum. 13. Transfer Function Models. 14. Vector Time Series Models. 15. State Space Models and the Kalman Filter. 16. Aggregation and Systematic Sampling in Time Series. 17. References. 18. Appendix.
1,497 citations
TL;DR: Singular spectrum analysis (SSA) is used in this article to estimate the lagged-covariance matrix of the processes studied, which is the basis of SSA.
1,334 citations