Enhancing the accuracy of a data-driven reconstruction of bivariate jump-diffusion models with corrections for higher orders of the sampling interval

TL;DR

This paper improves the accuracy of data-driven bivariate jump-diffusion models by deriving correction terms for higher-order moments, addressing sampling interval limitations in reconstructing complex dynamical systems.

Contribution

It introduces correction terms for higher-order conditional moments, significantly enhancing the reconstruction accuracy of jump-diffusion models from finite sampling data.

Findings

Correction terms improve model reconstruction accuracy

Finite sampling intervals negatively impact higher-order moment estimation

Enhanced methods better characterize complex dynamical interactions

Abstract

We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find that the inevitably finite sampling interval of time-series data negatively affects the reconstruction accuracy of higher-order conditional moments that are required to reconstruct the underlying jump-diffusion equations. We derive correction terms for conditional moments in higher orders of the sampling interval and demonstrate their suitability to strongly enhance the data-driven reconstruction accuracy.