In this paper, we discuss precise asymptotics for a new kind of moment convergence of the moving-average process $$X_k = sumlimits_{i = - infty }^infty {a_{i + k} varepsilon _i }$$, k a‰￥1, where {?μ i: a?’a?? i a??} is a doubly infinite sequence of independent identically distributed random variables with mean zero and the finiteness of variance, {?± i: a?’a?? i a??} is an absolutely summable sequence of real numbers, i.e., $$sumlimits_{i = - infty }^infty {left| {a_i } ight| infty }$$.
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