Singular Spectrum Analysis With Conditional Predictions for Real-Time State Estimation and Forecasting

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.