  It is a big challenge in the analysis of experimental data to disentangle the
unavoidable measurement noise from the intrinsic dynamical noise. Here we
present a general operational method to extract measurement noise from
stochastic time series, even in the case when the amplitudes of measurement
noise and uncontaminated signal are of the same order of magnitude. Our
approach is based on a recently developed method for a nonparametric
reconstruction of Langevin processes. Minimizing a proper non-negative function
the procedure is able to correctly extract strong measurement noise and to
estimate drift and diffusion coefficients in the Langevin equation describing
the evolution of the original uncorrupted signal. As input, the algorithm uses
only the two first conditional moments extracted directly from the stochastic
series and is therefore suitable for a broad panoply of different signals. To
demonstrate the power of the method we apply the algorithm to synthetic as well
as climatological measurement data, namely the daily North Atlantic Oscillation
index, shedding new light on the discussion of the nature of its underlying
physical processes.
