Moment bounds for stationary mixing sequences

Abstract

For an r>2 and a finite \(K,E\left| {\sum\limits_{j = 1}^n {X_j } } \right|^r \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } Kn^{r/2}\) (all n≧1) is obtained for a strictly stationary strong mixing sequence {Xj}. The convergence of rth(r>2) absolute moments in the central limit theorem for stationary φ-mixing and strong mixing sequences is also studied.