Estimating Semi-Nonparametric Densities by the Method of Moments

摘要

This article proposes the Method of Moments (MM) as a straightforward and accurate method to estimate financial returns densities when the Gram-Charlier asymptotic expansion is assumed as the data generating process. We show that MM provides very similar outcomes than Maximum Likelihood (ML) and overcomes both theoretical and empirical drawbacks of the latter, since it guarantees consistency regardless the density specification and also avoids possible convergence problems of the ML estimation algorithms. We compare the performance of both methods with an application to a large data set of daily returns of Dow Jones index.