Weak Convergence of Sums of Moving Averages in the $\alpha$-Stable Domain of Attraction

Abstract : Skorohod has shown that the convergence of sums of i.i.d. random variables to an alpha-stable Levy process, with 0alpha2, holds in the weak J sub 1 sense. It is shown that for sums of moving averages with at least 2 non-zero coefficients, weak J sub 1 convergence cannot hold, however, if the moving average coefficients are positive, weak M sub 1 convergence usually does hold, Keywords: bisection method; sequences (mathematics).