  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.
