A noise reduction method for multivariate time series

Abstract We generalize a noise reduction algorithm recently proposed by Grassberger and Schreiber to the case of multivariate time series. The corrections are given by a locally linear approximation using information from the past as well as from the future. The method is applied to the Ikeda map and the Lorenz system. If multivariate data is available the method is superior to scalar methods applied to the single coordinates, in particular with respect to the dynamical error.