Moment bounds for stationary mixing sequences

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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 {X j }. The convergence of rth(r>2) absolute moments in the central limit theorem for stationary φ-mixing and strong mixing sequences is also studied.