Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting. Issue 3 (13th February 2019)

• Record Type: Journal Article
• Authors: Ogrosky, H. Reed; Stechmann, Samuel N.; Chen, Nan; Majda, Andrew J.
• Is Part Of: Geophysical research letters. Volume 46:Issue 3(2019)
• Page Start: 1851
• Page End: 1860
• Publication Date: 2019-02-13
• Subjects: Geophysics -- Periodicals; Planets -- Periodicals; Lunar geology -- Periodicals; 550
• DOI: 10.1029/2018GL081100
• Languages: English
• ISSNs: 0094-8276

Abstract

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. Plain Language Summary: Singular spectrum analysis (SSA) is a powerful, commonly used technique to identify prominent patterns in observed data. However, SSA has some difficulty in providing accurate estimates near the endpoints of the time series, which can hinder its use in real time. A modified version of the SSA algorithm, referred to as SSA with conditional predictions, is presented to address these issues. SSA with conditional predictions provides a more accurate real‐time estimate of the leading modes of variability than the traditional method in a variety of tests. It can also be used to predict these patterns, and it is easy to implement. The uncertainty in the real‐time estimates of leading patterns is easily quantified as well. Key Points: Singular spectrum analysis (SSA) and extended empirical orthogonal function (EEOF) methods suffer from endpoint issues SSA with conditional predictions (SSA‐CP) is presented as a simple modification to improve real‐time estimates near endpoints Forecasts are also possible, including error estimates, and are optimal for Gaussian data and shown to also be skillful for non‐Gaussian data