Monitoring the parameter changes in general ARIMA time series models

We propose methods for monitoring the residuals of a fitted ARIMA or an autoregressive fractionally integrated moving average (ARFIMA) model in order to detect changes of the parameters in that model. We extend the procedures of Box & Ramirez (1992) and Ramirez (1992) and allow the differencing parameter, d to be fractional or integer. Test statistics are approximated by Wiener processes. We carry out simulations and also apply our method to several real time series. The results show that our method is effective for monitoring all parameters in ARFIMA models.