Analysis and data-driven reconstruction of bivariate jump-diffusion processes

Rydin Gorjao, L ; Sharif University of Technology | 2019

375 Viewed
  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.100.062127
  3. Publisher: American Physical Society , 2019
  4. Abstract:
  5. 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. © 2019 American Physical Society
  6. Keywords:
  7. Parameter estimation ; Bivariate time series ; Data-driven analysis ; Discontinuous process ; Integrated data ; Jump diffusion models ; Jump-diffusion process ; Non-parametric estimations ; Two dimensional diffusion ; Diffusion
  8. Source: Physical Review E ; Volume 100, Issue 6 , 2019 ; 24700045 (ISSN)
  9. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.062127