Geometric noise reduction for multivariate time series

We propose an algorithm for the reduction of observational noise in chaotic multivariate time series. The algorithm is based on a maximum likelihood criterion, and its goal is to reduce the mean distance of the points of the cleaned time series to the attractor. We give evidence of the convergence of the empirical measure associated with the cleaned time series to the underlying invariant measure, implying the possibility to predict the long run behavior of the true dynamics. (C) 2006 American Institute of Physics.