A Remark on Self-Normalization for Dependent Random Variables

Let (X_t, t ∈ Z) be a stationary process, and let S_n = ∑_{1⩽ i⩽n}X_i. In this paper, we consider the central limit theorem for the self-normalized sequence S_n/U_n, where U_n² = ∑_1⩽j⩽NY_j², Y_j = ∑_{(j−1)m<i⩽jm}X_i, n = mN. We show how such a self-normalization works for AR(1) and MA(q) processes.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 173–183, April–June, 2005.