An idealized "superparameterization", or abbreviated but dynamically explicit representation of small-scale influences on the conventionally resolved larger scales of a dynamical model, is constructed within the Lorenz '96 system. The feasibility of abstracting the greater portion of its information content using computationally much faster statistical summaries, or "emulators," is investigated through integration of a large number of ensemble forecasts. Both a simple regression emulator, and a Bayesian Gaussian process emulator are investigated. Even though based on an extremely small training-sample size, consistent with an assumed high computational expense for running a full superparameterization, some of the statistical emulator formulations perform nearly as well as the superparameterization forecast ensembles. As in previous studies, better forecast characteristics are generally achieved when autocorrelated random forcing is included, both in the otherwise deterministic superparameterization and in its statistical emulators.