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

Singular spectrum analysis (SSA) or extended empirical orthogonal function (EEOF) methods are 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 require, inaccurate reconstructions of leading modes near the endpoints can occur, which can hinder the use of these methods in real time. We present a modified version of the traditional SSA algorithm, referred to as SSA with conditional predictions (SSA-CP), to address these issues. Results will be presented from tests of SSA-CP 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 method. The method also provides predictions of the leading modes and is straightforward 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.