Discriminating dynamical from additive noise in the Van der Pol oscillator

Abstract

We address the distinction between dynamical and additive noise (AN) in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise (DN) only, while low values of the two are observed as soon as AN contaminates the signal. The method is presented through numerical tests on the well-known Van der Pol oscillator, including the chaotic case driven with a harmonic force. However, we give arguments according to which we expect a general validity for continuous-time systems.