Prediction of long-range-dependent discrete-time fractional Brownian motion process

We propose an approach to the linear minimum-mean-square-error (MMSE) prediction of a discrete-time fractional Brownian motion (DT-FBM) traffic arrival process, a long range dependent traffic model that well represents the characteristics of observed Internet traces. Linear multi-step forecasts of the future values of the DT-FBM process and the corresponding prediction errors are first derived. We then proposed sliding window finite-memory predictors suitable for practical implementation. Simulations using real-life traffic traces are performed to compare the proposed finite-memory DT-FBM predictors with fractional autoregressive integrated moving average predictors and an empirical predictor. We find that the multi-scale sliding window DT-FBM predictor achieves best performance on forecasting the future traffic level.