Symplectic geometry spectrum regression for prediction of noisy time series.
We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane QLD 4000, Australia.
Hong-Bo
HB
Xie
Graduate School of Biomedical Engineering, The University of New South Wales, Sydney NSW 2052, Australia.
Socrates
S
Dokos
School of Civil and Environmental Engineering, The University of New South Wales, Sydney NSW 2052, Australia.|Department of Land, Air and Water Resources, University of California, Davis, California 95616, USA.
Bellie
B
Sivakumar
ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane QLD 4000, Australia.
Kerrie
K
Mengersen