High-dimensional time series prediction using kernel-based Koopman mode regression

We propose a novel methodology for high-dimensional time series prediction based on the kernel method extension of data-driven Koopman spectral analysis, via the following methodological advances: (a) a new numerical regularization method, (b) a natural ordering of Koopman modes which provides a fas...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-11, Vol.90 (3), p.1785-1806
Main Authors: Hua, Jia-Chen, Noorian, Farzad, Moss, Duncan, Leong, Philip H. W., Gunaratne, Gemunu H.
Format: Article
Language:English
Subjects:
Artificial intelligence
Automotive Engineering
Autoregressive moving average
Classical Mechanics
Clients
Complex systems
Control
Data mining
Dynamical Systems
Econometrics
Engineering
Error analysis
Kernels
Machine learning
Mathematical models
Mechanical Engineering
Meteorology
Methodology
Model accuracy
Oceanography
Optimization
Original Paper
Regression analysis
Regularization
Regularization methods
Spectrum analysis
System identification
Time series
Vibration
Weather forecasting
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Summary:We propose a novel methodology for high-dimensional time series prediction based on the kernel method extension of data-driven Koopman spectral analysis, via the following methodological advances: (a) a new numerical regularization method, (b) a natural ordering of Koopman modes which provides a fast alternative to the sparsity-promoting procedure, (c) a predictable Koopman modes selection technique which is equivalent to cross-validation in machine learning, (d) an optimization method for selected Koopman modes to improve prediction accuracy, (e) prediction model generation and selection based on historical error measures. The prediction accuracy of this methodology is excellent: for example, when it is used to predict clients’ order flow time series of foreign exchange, which is almost random, it can achieve more than 10% improvement on root-mean-square error over auto-regressive moving average. This methodology also opens up new possibilities for data-driven modeling and forecasting complex systems that generate the high-dimensional time series. We believe that this methodology will be of interest to the community of scientists and engineers working on quantitative finance, econometrics, system biology, neurosciences, meteorology, oceanography, system identification and control, data mining, machine learning, and many other fields involving high-dimensional time series and spatio-temporal data.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3764-y