A note on moment bounds for strong mixing sequences

Abstract

For a g > 2 and finite K, E|∑ n i=1 X i | g ⩽ Kn g/2 (all n ⩾ 1) is obtained for a strictly stationary strong mixing or α-mixing sequence }0 X i } under less restrictive conditions than Yokoyama's (1980). Doob's argument (1953) for φ-mixing sequences of r.v.'s can be applied directly to α-mixing sequences and leads to improved results for moment bounds when g > 4. As applications, some limiting laws for α-mixing are discussed.