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

Abstract

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.