  Non-uniform sampling arises when an experimenter does not have full control
over the sampling characteristics of the process under investigation. Moreover,
it is introduced intentionally in algorithms such as Bayesian optimization and
compressive sensing. We argue that Stochastic Differential Equations (SDEs) are
especially well-suited for characterizing second order moments of such time
series. We introduce new initial estimates for the numerical optimization of
the likelihood, based on incremental estimation and initialization from
autoregressive models. Furthermore, we introduce model truncation as a purely
data-driven method to reduce the order of the estimated model based on the SDE
likelihood. We show the increased accuracy achieved with the new estimator in
simulation experiments, covering all challenging circumstances that may be
encountered in characterizing a non-uniformly sampled time series. Finally, we
apply the new estimator to experimental rainfall variability data.
