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Title:Inference for systems of stochastic differential equations from discretely sampled data: A numerical maximum likelihood approach PDF Logo
Authors:Lux, Thomas
Issue Date:2012
Series/Report no.:Kiel Working Paper 1781
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.
Subjects:stochastic differential equations
numerical maximum likelihood
Fokker-Planck equation
finite difference schemes
asset pricing
JEL:C58
G12
C13
Document Type:Working Paper
Appears in Collections:Publikationen von Forscherinnen und Forschern des IfW
Kieler Arbeitspapiere, IfW

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