2019/07/31 by Leonardo Rydin Gorjão, Jan Heysel, Klaus Lehnertz +1
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Bivariate analysis #Bivariate data #Computer science #Diffusion #Diffusion process #Econometrics #Image and Signal Denoising Methods #Jump #Jump diffusion #Jump process #Mathematical Biology Tumor Growth #Mathematics #Nonparametric statistics #Physics #Series (stratigraphy) #Statistical physics #Statistics #Stochastic processes and financial applications #msc:60G20 #nlin.AO #physics.data-an
paper · pdf · doi:10.1103/physreve.100.062127
published as Phys. Rev. E 100, 062127 (2019) · 13 pages, 9 figures
arxiv created 2019/09/27 · openalex publication_date 2019/12/20 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce the bivariate jump-diffusion process, consisting of two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, nonparametric 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.