  We compare two approaches to the predictive modeling of dynamical systems
from partial observations at discrete times. The first is continuous in time,
where one uses data to infer a model in the form of stochastic differential
equations, which are then discretized for numerical solution. The second is
discrete in time, where one directly infers a discrete-time model in the form
of a nonlinear autoregression moving average model. The comparison is performed
in a special case where the observations are known to have been obtained from a
hypoelliptic stochastic differential equation. We show that the discrete-time
approach has better predictive skills, especially when the data are relatively
sparse in time. We discuss open questions as well as the broader significance
of the results.
