Statistical Papers

, Volume 60, Issue 1, pp 313–347 | Cite as

Estimation methods for the LRD parameter under a change in the mean

  • Aeneas Rooch
  • Ieva ZeloEmail author
  • Roland Fried
Regular Article


When analyzing time series which are supposed to exhibit long-range dependence (LRD), a basic issue is the estimation of the LRD parameter, for example the Hurst parameter \(H \in (1/2, 1)\). Conventional estimators of H easily lead to spurious detection of long memory if the time series includes a shift in the mean. This defect has fatal consequences in change-point problems: Tests for a level shift rely on H, which needs to be estimated before, but this estimation is distorted by the level shift. We investigate two blocks approaches to adapt estimators of H to the case that the time series includes a jump and compare them with other natural techniques as well as with estimators based on the trimming idea via simulations. These techniques improve the estimation of H if there is indeed a change in the mean. In the absence of such a change, the methods little affect the usual estimation. As adaption, we recommend an overlapping blocks approach: If one uses a consistent estimator, the adaption will preserve this property and it performs well in simulations.


Hurst parameter Estimation Jump Long-range dependence Long memory Change-point problems 

Mathematics Subject Classification




The financial support of the Deutsche Forschungsgemeinschaft (SFB 823, “Statistical modelling of nonlinear dynamic processes”) is gratefully acknowledged. We would like to thank two referees for their constructive comments which improved the presentation of our work considerably.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Fakultät für StatistikTechnische Universität DortmundDortmundGermany

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