Gram–Charlier densities: Maximum likelihood versus the method of moments
AbstractThis paper compares two alternative estimation methods for estimating the density underlying financial returns specified in terms of a finite Gram–Charlier (GC) expansion. Maximum likelihood (ML) is the most widely employed method despite the fact that it is only consistent under the Gaussian or the true density, and usually involves convergence problems. Alternatively, the method of moments (MM) is a natural and straightforward procedure, although positivity is only guaranteed in the asymptotic expansion. We show an example for estimating daily returns of the Dow Jones Index with a very long data set, illustrating that both ML and MM yield similar outcomes. Therefore the MM applied to GC densities should be considered as an accurate tool for risk management and forecasting.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 51 (2012)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/locate/inca/505554
Semi-nonparametric method; Maximum likelihood; Method of moments; Financial returns density; Value at risk;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
- G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
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