  We present a novel methodology based on filtered data and moving averages for
estimating effective dynamics from observations of multiscale systems. We show
in a semi-parametric framework of the Langevin type that our approach is
asymptotically unbiased with respect to the theory of homogenization. Moreover,
we demonstrate on a range of challenging numerical experiments that our method
is accurate in extracting coarse-grained dynamics from multiscale data. In
particular, the estimators we propose are more robust and require less
knowledge of the full model than the standard technique of subsampling, which
is widely employed in practice in this setting.
