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Fitting of the parameters of a Phase Type (PH) distribution or a Markovian Arrival Process (MAP) according to some quantities of measured data streams is still a challenge. This paper presents a new approach which computes in two steps for a set of moments and joint moments for an acyclic PH distribution that is expanded into a MAP. In contrast to other known approaches, parameters are computed to minimize the weighted squared difference between the measured moments and the moments of the resulting PH distribution or MAP. The proposed approach is very flexible and allows one to generate a MAP of a predefined order to approximate a given set of moments and joint moments. It is shown that the approximation is often sufficiently accurate even with MAPs of a moderate size. However, we also show that the practical applicability of the approach is limited since the exact determination of higher order moments from traces requires an extremely high effort.