TWO METHODS TO GENERATE CENTERED DISTRIBUTIONS CONTROLLING SKEWNESS AND KURTOSIS COEFFICIENTS

Pierre-Eric Treyens (1, 2)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 CIREQ - Centre interuniversitaire de recherche en économie quantitative

Whatever the econometric model which we study; any simulation requires a perfectly definite DGP. Thus, even if all software can generate standard normal distributions, we need methods not programmed to control higher moments. For all these methods, we need to estimate the parameters connected to the desired values of the higher moments. Within the framework of Monte Carlo experiments, the computing times of this estimate are then not very important. Indeed, once these parameters estimated, we can re-use them and the computing time of simulations does not suffer from it. On the other hand, for a parametric bootstrap which would consider the first four moments, the computing time is then multiplied by the number of desired simulations. So we understand the importance to provide a method which makes it possible to find the parameters attached to the first four estimated moments as quickly as possible. So, we must trade off between speed and possibilities of the method. The goal of this paper is to provide two new methods which control these first four moments and to compare their speed with that of the already existing methods.

Mots clés: Skewness; kurtosis; simulations; econometrics

Domaines: Economies et finances

Pierre-Eric Treyens. TWO METHODS TO GENERATE CENTERED DISTRIBUTIONS CONTROLLING SKEWNESS AND KURTOSIS COEFFICIENTS. 2007. ⟨halshs-00353291⟩