ON COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES WITH APPLICATION TO MOVING AVERAGE PROCESSES

Let {$Y_i$,-$\infty$ < i < $\infty$} be a doubly infinite sequence of i.i.d. random variables with E|$Y_1$| < $\infty$, {$a_{ni}$,-$\infty$ < i < $\infty$ n $\geq$ 1} an array of real numbers. Under some conditions on {$a_{ni}$}, we obtain necessary and sufficient conditions for $\sum\;_{n=1}^{\infty}\frac{1}{n}P(|\sum\;_{i=-\infty}^{\infty}a_{ni}(Y_i-EY_i)|$>$n{\epsilon})$<{\infty}$. We examine whether the result of Spitzer [11] holds for the moving average process, and give a partial solution.