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

Aeneas Rooch (), Ieva Zelo () and Roland Fried ()
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Aeneas Rooch: Ruhr-Universität Bochum
Ieva Zelo: Technische Universität Dortmund
Roland Fried: Technische Universität Dortmund

Statistical Papers, 2019, vol. 60, issue 1, No 16, 313-347

Abstract: 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 $$H \in (1/2, 1)$$ H ∈ ( 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.

Keywords: Hurst parameter; Estimation; Jump; Long-range dependence; Long memory; Change-point problems; 62M10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00362-016-0839-7

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