Almost sure central limit theorem for self-normalized partial sums of ρ−-mixing sequences

Feng Xu and Qunying Wu

Statistics & Probability Letters, 2017, vol. 129, issue C, 17-27

Abstract: Let {X,Xn}n∈N be a weakly stationary sequence of ρ−-mixing random variables. We discussed the almost sure central limit theorem for the self-normalized partial sums Sn/βVn, where Sn=∑i=1nXi, Vn2=∑i=1nXi2, constant β>0. Our results generalize and improve those on almost sure central limit theorems obtained by previous authors from the independent case to ρ−-mixing sequences and from dk=1/k to dk=lnckclexp(lnαck),0≤α<1/2.

Keywords: ρ−-mixing sequences; Self-normalized partial sums; Almost sure central limit theorem (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.04.023

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