Inference for Systems of Stochastic Differential Equations from Discretely Sampled data: A Numerical Maximum Likelihood Approach
AbstractMaximum 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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Bibliographic InfoPaper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1781.
Length: 37 pages
Date of creation: Jul 2012
Date of revision:
stochastic differential equations; numerical maximum likelihood; Fokker-Planck equation; finite difference schemes; asset pricing;
Find related papers by JEL classification:
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-23 (All new papers)
- NEP-ECM-2012-07-23 (Econometrics)
- NEP-ORE-2012-07-23 (Operations Research)
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