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# On the efficiency of the sample mean in long memory noise

**Alexander Samarov
**

Murad S. Taqqu

### Abstract:

*When estimating the unknown mean of a stationary time series the best linear unbiased estimator is often a significantly better estimator than the ordinary least squares estimates . The relative
efficiency of these two estimators is investigated for time series whose
spectrum behaves like a power at the origin (e.g. fractional Gaussian noise
and fractional ARIMA).
**
*