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  • 1 Russian-Armenian University, 123 Hovsep Emin St, Yerevan 0051, Armenia
  • 2 Boston University, 111 Cummington Mall, Boston, MA 02215, USA
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In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

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