@techreport{Lux2012Inference,
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.},
address = {Kiel},
author = {Thomas Lux},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C58; G12; C13; 330; stochastic differential equations; numerical maximum likelihood; Fokker-Planck equation; finite difference schemes; asset pricing; Maximum-Likelihood-Methode; Analysis; Stochastischer Prozess; Theorie; B\"{o}rsenkurs; Anlageverhalten; Sch\"{a}tzung; Deutschland},
language = {eng},
number = {1781},
publisher = {Kiel Institute for the World Economy (IfW)},
title = {Inference for systems of stochastic differential equations from discretely sampled data: A numerical maximum likelihood approach},
type = {Kiel Working Paper},
url = {http://hdl.handle.net/10419/60335},
year = {2012}
}
