  We study the problem of parameter estimation for time-series possessing two,
widely separated, characteristic time scales. The aim is to understand
situations where it is desirable to fit a homogenized singlescale model to such
multiscale data. We demonstrate, numerically and analytically, that if the data
is sampled too finely then the parameter fit will fail, in that the correct
parameters in the homogenized model are not identified. We also show,
numerically and analytically, that if the data is subsampled at an appropriate
rate then it is possible to estimate the coefficients of the homogenized model
correctly.
