Inference for Systems of Stochastic Differential Equations from Discretely Sampled data: A Numerical Maximum Likelihood Approach
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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- Thomas Lux, 2007.
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- Lux, Thomas, 2008. "Rational forecasts or social opinion dynamics? Identification of interaction effects in a business climate survey," Economics Working Papers 2008,07, Christian-Albrechts-University of Kiel, Department of Economics.
- Thomas Lux, 2008. "Rational Forecasts or Social Opinion Dynamics? Identification of Interaction Effects in a Business Climate Survey," Kiel Working Papers 1424, Kiel Institute for the World Economy.
- Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08.
- Thomas Lux, 2011. "Sentiment dynamics and stock returns: the case of the German stock market," Empirical Economics, Springer, vol. 41(3), pages 663-679, December.
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