Abstract: | The paper obtains a functional limit theorem for the empirical process of a stationary moving average process Xt with i.i.d. innovations belonging to the domain of attraction of a symmetric -stable law, 1<<2, with weights bj decaying as j−β, 1<β<2/. We show that the empirical process (normalized by N1/β) weakly converges, as the sample size N increases, to the process cx+L++cx−L−, where L+,L− are independent totally skewed β-stable random variables, and cx+,cx− are some deterministic functions. We also show that, for any bounded function H, the weak limit of suitably normalized partial sums of H(Xs) is an β-stable Lévy process with independent increments. This limiting behavior is quite different from the behavior of the corresponding empirical processes in the parameter regions 1/<β<1 and 2/<β studied in Koul and Surgailis (Stochastic Process. Appl. 91 (2001) 309) and Hsing (Ann. Probab. 27 (1999) 1579), respectively. |