A symplectic geometry-based method for nonlinear time series decomposition and prediction

摘要

We present a technique to decompose a time series into the sum of a small number of independent and interpretable components based on symplectic geometry theory. The proposed symplectic geometry spectrum analysis technique consists of embedding, symplectic QR decomposition of the matrix into an orthogonal matrix and a triangular matrix, grouping, and diagonal averaging steps. As an example application, the noisy Lorenz series demonstrate the effectiveness of this technique in nonlinear prediction.