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We study by computer simulation the 'Hawkes process' that was proposed in a recent paper by Crane and Sornette (2008 Proc. Natl Acad. Sci. USA 105 15649) as a plausible model for the dynamics of YouTube video viewing numbers. We test the claims made there that robust identification is possible for classes of dynamic response following activity bursts. Our simulated time series for the Hawkes process indeed fall into the different categories predicted by Crane and Sornette. However, the Hawkes process gives a much narrower spread of decay exponents than the YouTube data, suggesting limits to the universality of the Hawkes-based analysis.