Estimation methods for the LRD parameter under a change in the mean
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Date
2016
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Abstract
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 2 (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.
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Keywords
Hurst parameter, change-point problems, long memory, long-range dependence, jump, estimation