Kiel Working Papers, Kiel Institute for World Economics
No 1781:
Inference for Systems of Stochastic Differential Equations from Discretely Sampled data: A Numerical Maximum Likelihood Approach
Thomas Lux
Abstract: 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
Keywords: stochastic differential equations, numerical maximum likelihood, Fokker-Planck equation, finite difference schemes, asset pricing; (follow links to similar papers)
JEL-Codes: C58,; G12,; C13; (follow links to similar papers)
37 pages, July 2012
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