Spectral estimates and stable processes

Let be a discrete time moving average process based on i.i.d. symmetric random variables {Zt} with a common distribution function from the domain of normal attraction of a p-stable law (0 < p < 2). We derive the limit distribution of the normalized periodogram . This generalizes the classical result for p = 2. In contrast to the classical case, for values 0 < [lambda]1 < ... < [lambda]m < [pi] the periodogram ordinates In, X([lambda]i), I = 1, ..., m, are not asymptotically independent.