Precise asymptotics in complete moment convergence of moving-average processes

In this paper, we discuss moving-average process , where {[var epsilon]i;-[infinity]<i<[infinity]} is a doubly infinite sequence of i.i.d random variables with mean zeros and finite variances, {ai;-[infinity]<i<[infinity]} is an absolutely summable sequence of real numbers. Set . Suppose E[var epsilon]13<[infinity], we prove that, if E[var epsilon]1r<[infinity], for 1<p<2 and r>1+p/2, then where Z has a normal distribution with mean 0 and variance .