Accurate Characterization of Non-Uniformly Sampled Time Series using Stochastic Differential Equations
This work addresses the challenge of analyzing irregularly sampled data, which is common in fields like climate science and optimization algorithms, but it appears incremental as it builds on existing SDE frameworks with specific improvements.
The paper tackled the problem of characterizing non-uniformly sampled time series by proposing new methods for optimizing Stochastic Differential Equations (SDEs), including initial estimates and model truncation, and demonstrated increased accuracy in simulations and applied it to rainfall variability data.
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.