Generalized Multivariate Singular Spectrum Analysis for Nonlinear Time Series De-Noising and Prediction

Singular spectrum analysis and its multivariate or multichannel singular spectrum analysis (MSSA) variant are effective methods for time series representation, denoising and prediction, with broad application in many fields. However, a key element in MSSA is singular value decomposition of a high-dimensional matrix stack of component matrices, where the spatial (structural) information among multivariate time series is lost or distorted. This vector-space model also leads to difficulties including high dimensionality, small sample size, and numerical instability when applied to multi-dimensional time series. We present a generalized multivariate singular spectrum analysis (GMSSA) method to simultaneously decompose multivariate time series into constituent components, which can overcome the limitations of conventional multivariate singular spectrum analysis. In addition, we propose a SampEn-based method to determine the dominant components in GMSSA. We demonstrate the effectiveness and efficiency of GMSSA to simultaneously de-noise multivariate time series for attractor reconstruction, and to predict both simulated and real-world multivariate noisy time series.