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We propose a solution to the Web server load prediction problem based on a hierarchical framework with multiple time scales. This framework leads to adaptive procedures that provide both long-term (in days) and short-term (in minutes) predictions with simultaneous confidence bands which accommodate not only serial correlation but also heavy-tailedness, and non-stationarity of the data. The long-term load is modeled as a dynamic harmonic regression (DHR), the coefficients of which evolve according to a random walk, and are tracked using sequential Monte Carlo (SMC) algorithms; whereas, the short-term load is predicted using an autoregressive model, whose parameters are also estimated using SMC techniques. We evaluate our method using real world web workload data.