On distinguishing multiple changes in mean and long-range dependence using local Whittle estimation

It is well known that changes in mean superimposed by a short-range dependent series can he confused easily with long-range dependence. A procedure to distinguish the two phenomena is introduced. The proposed procedure is based on the local Whittle estimation of the long-range dependence parameter applied to the series after removing changes in mean, and comparing the results to those obtained through the available CUSUM-like approaches. According to the proposed procedure, for example, volatility series in finance seem more consistent with the changes-in-mean models whereas hydrology and telecommunication series are more in line with long-range dependence. As part of this work, a new method based on the local Whittle estimation to find the number of breaks is also introduced and its consistency is proved for the changes-in-mean models.