Prediction of chaotic systems with multidimensional recurrent least squares support vector machines

In this paper, we propose a multidimensional version of recurrent leastsquares support vector machines (MDRLS-SVM) to solve the problem about theprediction of chaotic system. To acquire better prediction performance, thehigh-dimensional space, which provides more information on the system thanthe scalar time series, is first reconstructed utilizing Takens's embeddingtheorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in thehigh-dimensional space, and the prediction performance can be improved fromthe point of view of reconstructed embedding phase space. In addition, theMDRLS-SVM algorithm is analysed in the context of noise, and we also findthat the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.