Optimal time delay embedding for nonlinear time series modeling

摘要

When building linear or nonlinear models one is faced with the problem ofselecting the best set of variable with which to predict the future dynamics.In nonlinear time series analysis the problem is to select the correct timedelays in the time delay embedding. We propose a new technique which canquantify the suitability of a particular set of variables and we suggests acomputationally efficient scheme to determine the best non-uniform time delayembedding for modeling of time series. Our results are based on the assumptionthat, in general, the variables which give the best local constant model willalso give the best nonlinear model. In a wide variety of experimental andsimulated systems we find that this method produces dynamics that are morerealistic and predictions that are more accurate than standard uniformembeddings.