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http://hdl.handle.net/10419/60335
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| Title: | | Inference for systems of stochastic differential equations from discretely sampled data: A numerical maximum likelihood approach  |
| 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: | | Economists Online Publikationen von Forscherinnen und Forschern des IfW Kieler Arbeitspapiere, IfW
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