B1351
Title: Estimation methods for the long memory parameter under a change in the mean
Authors: Ieva Zelo - TU Dortmund (Germany) [presenting]
Aeneas Rooch - Ruhr-Universitaet Bochum (Germany)
Roland Fried - TU Dortmund University (Germany)
Abstract: Time series analysis is often based on the assumption of stationarity. However, the estimation of any time-constant parameter is affected heavily by the presence of a change in the mean. When analyzing time series which are supposed to exhibit long memory, a basic issue is the estimation of the long memory parameter, for example the Hurst parameter $H$. 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 techniques to adapt estimators of $H$ to the case that the time series includes a jump and compare them via simulations. Based on our results, we recommend an overlapping blocks approach: If one uses a consistent estimator, the adaption will preserve this property and it performs well in simulations. The blocks technique is also useful for the estimation of other parameters, such as the variance, as will be illustrated.
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