Singular Spectrum Analysis With Conditional Predictions for Real‐Time State Estimation and Forecasting - H. Reed Ogrosky; Samuel N. Stechmann; Nan Chen; Andrew J. Majda (Geophysical Research Letters)
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.