In this paper, we propose a traffic model for the characterization of VBR MPEG-coded video streams. This model provides the means to generate synthetic MPEG streams that can be used in performance studies of ATM networks. The model is appropriately fitted to three long empirical video sequences taken from different movies. We use multiple components to model bit rate variations in an MPEG stream. These components have different time scales. Long-term variations in the bit rate are captured at the scene level. Within a scene, the sizes of I frames tend to slightly fluctuate around some average. Hence, we measure the activity of the scene by the average size of I frames in that scene. This average varies from one scene to another, and its randomness is reasonably approximated by a lognormal distribution. For a given scene, the fluctuations of the sizes of I frames about- their mean are modeled as an AR(2) time series. Finally, we show that the sizes of P and B frames can be appropriately fitted by lognormal distributions, with corresponding parameters. Using the compression pattern, the complete frame size sequence is formed by intermixing three subsequences, each of which describes the frame size sequence for a particular frame type. The validity of the model is demonstrated by the similarity between a synthetic stream and an actual trace, in terms of the correlation structure, the marginal distribution, the sample paths, and more importantly, the queueing performance. (Also cross-referenced as UMIACS-TR-95-120)