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

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  • Thomas Lux
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    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

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    File URL: https://www.ifw-members.ifw-kiel.de/publications/inference-for-systems-of-stochastic-differential-equations-from-discretely-sampled-data-a-numerical-maximum-likelihood-approach-1/12Inference%20for%20systems.pdf
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    Bibliographic Info

    Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1781.

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    Length: 37 pages
    Date of creation: Jul 2012
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    Handle: RePEc:kie:kieliw:1781

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    Keywords: stochastic differential equations; numerical maximum likelihood; Fokker-Planck equation; finite difference schemes; asset pricing;

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