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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).