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Non-uniform sampling arises when an experimenter does not have full controlover the sampling characteristics of the process under investigation. Moreover,it is introduced intentionally in algorithms such as Bayesian optimization andcompressive sensing. We argue that Stochastic Differential Equations (SDEs) areespecially well-suited for characterizing second order moments of such timeseries. We introduce new initial estimates for the numerical optimization ofthe likelihood, based on incremental estimation and initialization fromautoregressive models. Furthermore, we introduce model truncation as a purelydata-driven method to reduce the order of the estimated model based on the SDElikelihood. We show the increased accuracy achieved with the new estimator insimulation experiments, covering all challenging circumstances that may beencountered in characterizing a non-uniformly sampled time series. Finally, weapply the new estimator to experimental rainfall variability data.

Accurate Characterization of Non-Uniformly Sampled Time Series using Stochastic Differential Equations