Break detection in nonstationary strongly dependent long time series

We consider the problem of fitting a piecewise fractional autoregressive integrated moving average model to strongly dependent signals with large data. The number as well as the locations of structural break points, the model order and the parameters of each regime are assumed to be unknown. A four-step method based on distances between parameter estimates is proposed, to avoid the optimization problem which criterion based methods may be trapped in when there are a lot of data in the signal series. Monte Carlo simulations show the effectiveness of the method with different distances and an application to real traffic data modelling is considered.