This paper presents the results of measuring the Hurst parameter for a wide selection of video sequences encoded with H.264 compression with constant quantization index. Six techniques for measuring the Hurst parameter are compared and used on the source data. The Hurst parameter was found to have an average value of 0.9, with a minimum of about 0.8, over the whole set of sequences, indicating the presence of a significant degree of long range dependence in the statistics of the coded data. It is known that traffic with long range dependence causes increased queue length and more packet loss than traffic with only short range dependence. We conclude that if video is to be transmitted at near constant quality, the fact that the resulting data has a significant degree of long range dependence must be taken into account when provisioning the traffic in a network in order to meet quality of service guarantees.