In the Irish electricity market participants declare their true marginal costs and therefore the Shadow Price alone does not guarantee that generators will recover their fixed running costs. The so-called Uplift complements the price and ensures that the generators recover their total costs. The aim of this paper is to review purely stochastic features of the Uplift and make an attempt to simulate a new process reconstructing the original data characteristics. We propose two alternative algorithms basing on the Uplift wait-jump structure as well as daily and annual seasonality. Presented results show that this kind of reconstruction is possible up to a quantitatively comparable degree.