  We construct a novel estimator for the diffusion coefficient of the limiting
homogenized equation, when observing the slow dynamics of a multiscale model,
in the case when the slow dynamics are of bounded variation. Previous research
suggests subsampling the data on fixed intervals and computing the
corresponding quadratic variation. However, to achieve optimality, this
approach requires knowledge of scale separation variable $\epsilon$. Instead,
we suggest computing the quadratic variation corresponding to the local extrema
of the slow process. Our approach results to a natural subsampling and avoids
the issue of choosing a subsampling rate. We prove that the estimator is
asymptotically unbiased and we numerically demonstrate that its $L_2$-error is
of order ${\mathcal O}(\epsilon^2)$.
