A Method to Generate Multivariate Data with the Desired Moments

We show how it is possible to generate multivariate data which has moments arbitrary close to the desired ones. They are generated as linear combinations of variables with known theoretical moments. It is shown how to derive the weights of the linear combinations in both the univariate and the multivariate setting. The use in bootstrapping is discussed and the method is exemplified with a Monte Carlo simulation where the importance of the ability of generating data with control of higher moments is shown.