For the purpose of provisioning bandwidth for Internet access, we need to model the trafic at large time scales, over which the trafJic shows evident periodicity, long correlation and a non-Gaussian marginal distribution. To capture these characteristics simultaneously, in this paper we use a periodicity transform to identify the most sign$cant periods of the trafic and use an autoregressive time series to capture the autocorrelation and apply the G-and-H distribution to model the marginal distribution. A prediction-based bandwidth provisioning scheme is proposed and many experimental results on real Internet traces are also provided. Key words: Internet trafic, periodicity