Monitoring Mean and Variance Change-Points in Long-Memory Time Series

This paper proposes two ratio-type statistics to sequentially detect mean and variance change-points in the long-memory time series. The limiting distributions of monitoring statistics under the no change-point null hypothesis, alternative hypothesis as well as change-point misspecified hypothesis are proved. In particular, a sieve bootstrap approximation method is proposed to determine the critical values. Simulations indicate that the new monitoring procedures have better finite sample performance than the available off-line tests when the change-point nears to the beginning time of monitoring, and can discriminate between mean and variance change-point. Finally, the authors illustrate their procedures via two real data sets: A set of annual volume of discharge data of the Nile river, and a set of monthly temperature data of northern hemisphere. The authors find a new variance change-point in the latter data.