A local stationary long-memory model for internet traffic

We present in this paper a piecewise fractional autoregressive integrated moving average (FARIMA) model and a procedure to fit this model to local-stationary traffic data. The procedure consists in finding the number as well as the locations of structural break points in the series and estimating the orders and the parameters of each segment. The effectiveness of the procedure is illustrated by Monte Carlo simulations. An application to real internet traffic data is considered and shows that the piecewise FARIMA model is able to capture the non-stationarity and the long-memory of these data.