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We propose a traffic fitting algorithm for Markovian Arrival Processes (MAPs) that can capture statistics of any order of interarrival times. By studying real traffic traces, we show that matching higher order properties, in addition to first and second order descriptors, results in increased queueing prediction accuracy with respect to other algorithms that only match the mean, coefficient of variation, and autocorrelations. The result promotes the idea of modeling traffic traces using the interarrival time process instead of the counting process that is more frequently employed in previous work, but for which higher order moments are difficult to manipulate. We proceed by first characterizing the general properties of MAPs using a spectral approach. Based on this characterization, we show how different MAP processes can be combined together using Kronecker products to define a larger MAP with predefined properties of interarrival times. We then devise an algorithm that is based on this Kronecker composition and can accurately fit traffic traces. The algorithm employs nonlinear optimization programs that can be customized to fit an arbitrary number of moments and to meet the desired cost-accuracy tradeoff. Numerical results of the fitting algorithm on real HTTP and TCP traffic data, such as the Bellcore Aug89 trace, indicate that the proposed fitting methods achieve increased prediction accuracy with respect to other state-of-the-art fitting methods.