Cell loss is an important measure of quality of service (QoS) in ATM networks. Cell loss performance of ATM elements handling bursty sources must be evaluated in order to provide guaranteed QoS to users and to dimension network resources correctly. In this paper, we make a comparative study of two fitting algorithms for 2-MMPP ATM traffic models, both based on cell interarrival times: one fits the cumulative distribution and auto-covariance functions and the other fits the first three moments and auto-covariance function. The 2-MMPP is then evaluated as an approximation to 3-MMPP, 5-MMPP, IPP, IDP, Hyper-Exponential On-Off and Self-Similar traffic sources. The usefulness of both fitting procedures for cell loss prediction is evaluated and compared. The proposed algorithms can be used in the characterisation of ATM traffic streams and in connection admission control procedures.