Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting
Abstract Singular spectrum analysis (SSA) or extended empirical orthogonal function methods are powerful, commonly used data‐driven techniques to identify modes of variability in time series and space‐time data sets. Due to the time‐lagged embedding, these methods can provide inaccurate reconstructi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-02-01
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| Series: | Geophysical Research Letters |
| Online Access: | https://doi.org/10.1029/2018GL081100 |
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| _version_ | 1850134726207078400 |
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| author | H. Reed Ogrosky Samuel N. Stechmann Nan Chen Andrew J. Majda |
| author_facet | H. Reed Ogrosky Samuel N. Stechmann Nan Chen Andrew J. Majda |
| author_sort | H. Reed Ogrosky |
| collection | DOAJ |
| description | Abstract Singular spectrum analysis (SSA) or extended empirical orthogonal function methods are powerful, commonly used data‐driven techniques to identify modes of variability in time series and space‐time data sets. Due to the time‐lagged embedding, these methods can provide inaccurate reconstructions of leading modes near the endpoints, which can hinder the use of these methods in real time. A modified version of the traditional SSA algorithm, referred to as SSA with conditional predictions (SSA‐CP), is presented to address these issues. It is tested on low‐dimensional, approximately Gaussian data, high‐dimensional non‐Gaussian data, and partially observed data from a multiscale model. In each case, SSA‐CP provides a more accurate real‐time estimate of the leading modes of variability than the traditional reconstruction. SSA‐CP also provides predictions of the leading modes and is easy to implement. SSA‐CP is optimal in the case of Gaussian data, and the uncertainty in real‐time estimates of leading modes is easily quantified. |
| format | Article |
| id | doaj-art-0e1b2d6ea10a4cc18696493d8e35e75b |
| institution | OA Journals |
| issn | 0094-8276 1944-8007 |
| language | English |
| publishDate | 2019-02-01 |
| publisher | Wiley |
| record_format | Article |
| series | Geophysical Research Letters |
| spelling | doaj-art-0e1b2d6ea10a4cc18696493d8e35e75b2025-08-20T02:31:39ZengWileyGeophysical Research Letters0094-82761944-80072019-02-014631851186010.1029/2018GL081100Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and ForecastingH. Reed Ogrosky0Samuel N. Stechmann1Nan Chen2Andrew J. Majda3Department of Mathematics and Applied Mathematics Virginia Commonwealth University Richmond VA USADepartment of Mathematics University of Wisconsin‐Madison Madison WI USADepartment of Mathematics University of Wisconsin‐Madison Madison WI USADepartment of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences New York University New York NY USAAbstract Singular spectrum analysis (SSA) or extended empirical orthogonal function methods are powerful, commonly used data‐driven techniques to identify modes of variability in time series and space‐time data sets. Due to the time‐lagged embedding, these methods can provide inaccurate reconstructions of leading modes near the endpoints, which can hinder the use of these methods in real time. A modified version of the traditional SSA algorithm, referred to as SSA with conditional predictions (SSA‐CP), is presented to address these issues. It is tested on low‐dimensional, approximately Gaussian data, high‐dimensional non‐Gaussian data, and partially observed data from a multiscale model. In each case, SSA‐CP provides a more accurate real‐time estimate of the leading modes of variability than the traditional reconstruction. SSA‐CP also provides predictions of the leading modes and is easy to implement. SSA‐CP is optimal in the case of Gaussian data, and the uncertainty in real‐time estimates of leading modes is easily quantified.https://doi.org/10.1029/2018GL081100 |
| spellingShingle | H. Reed Ogrosky Samuel N. Stechmann Nan Chen Andrew J. Majda Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting Geophysical Research Letters |
| title | Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting |
| title_full | Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting |
| title_fullStr | Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting |
| title_full_unstemmed | Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting |
| title_short | Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting |
| title_sort | singular spectrum analysis with conditional predictions for real time state estimation and forecasting |
| url | https://doi.org/10.1029/2018GL081100 |
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