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Variance of partial sums of stationary sequences. (English) Zbl 1291.60068

The authors give necessary and sufficient conditions for the variance of partial sums of centered sequences of weakly stationary random variables to be regularly varying of index \(\gamma\) at infinity. The authors derive lower and upper bounds for the variance of partial sums and use them to prove the main result of this paper.

MSC:

60G10 Stationary stochastic processes
42A24 Summability and absolute summability of Fourier and trigonometric series
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