  We introduce the bivariate jump-diffusion process, comprising two-dimensional
diffusion and two-dimensional jumps, that can be coupled to one another. We
present a data-driven, non-parametric estimation procedure of higher-order (up
to 8) Kramers-Moyal coefficients that allows one to reconstruct relevant
aspects of the underlying jump-diffusion processes and to recover the
underlying parameters. The procedure is validated with numerically integrated
data using synthetic bivariate time series from continuous and discontinuous
processes. We further evaluate the possibility of estimating the parameters of
the jump-diffusion model via data-driven analyses of the higher-order
Kramers-Moyal coefficients, and the limitations arising from the scarcity of
points in the data or disproportionate parameters in the system.
