Working Paper

Inference for Systems of Stochastic Differential Equations from Discretely Sampled data: A Numerical Maximum Likelihood Approach

Author

  • Thomas Lux
Publication Date

Maximum likelihood estimation of discretely observed diffusion processes is mostly hampered by the lack of a closed form solution of the transient density. It has recently been argued that a most generic remedy to this problem is the numerical solution of the pertinent Fokker-Planck (FP) or forward Kol- mogorov equation. Here we expand extant work on univariate diffusions to higher dimensions. We find that in the bivariate and trivariate cases, a numerical solution of the FP equation via alternating direction finite difference schemes yields results surprisingly close to exact maximum likelihood in a number of test cases.

After providing evidence for the effciency of such a numerical approach, we illustrate its application for the estimation of a joint system of short-run and medium run investor sentiment and asset price dynamics using German stock market data.

Info

JEL Classification
C58, G12, C13

Key Words

  • finite difference schemes
  • Fokker-Planck equation
  • numerical maximum likelihood
  • Stochastic differential equations