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

TL;DR

This paper presents a novel approach using Stochastic Differential Equations to accurately characterize non-uniformly sampled time series, improving estimation accuracy through new initialization and model truncation methods, with applications to rainfall data.

Contribution

Introduces new initialization and model truncation techniques for SDE-based estimation of non-uniformly sampled time series, enhancing accuracy and applicability.

Findings

Improved estimator accuracy in simulations.

Effective model order reduction via data-driven truncation.

Successful application to rainfall variability data.

Abstract

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.