Influence of noise on the averaged false neighbors method for analyzing time series

This paper deals with the influence of noise on the averaged false neighbors method (AFN) proposed by L. Cao for analyzing time series and describing the dynamical properties of their underlying process. First, we give a theoretical justification of the AFN method results for a pure random time series (white gaussian noise). Then we present some numerical experiments corresponding to different known chaotic processes corrupted by noise. Simulations on real measured data are also presented. Eventually, after discussing these simulations, we are led to state some practical results on the critical noise level not to be exceeded for getting usable results of the AFN algorithm.