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This paper investigates the application of discrete-time statistically self-similar systems to modeling variable-bit rate (VBR) video traces. Potential application to classifying scenes in VBR video is explored. The work is motivated by the fact that while VBR video has been characterized as self-similar by various researchers, models based on self-similarity considerations have not been previously studied. This paper also shows that using heavy-tailed inputs these models can be used to match both the scene density time-series autocorrelation as well as its marginal distribution.