C. Kluppelberg et T. Mikosch, SOME LIMIT THEORY FOR THE SELF-NORMALIZED PERIODOGRAM OF STABLE PROCESSES, Scandinavian journal of statistics, 21(4), 1994, pp. 485-491
Let X(t) = Sigma(j)(infinity) = (-infinity) psi(j)Z(t-j) be a discrete
moving average process based on i.i.d. random variables (Z(t),)(t eps
ilon Z) with common distribution function from the domain of normal at
traction of a p-stable law (0 < p less than or equal to 2). We prove w
eak convergence of the self-normalised periodogram [GRAPJICS] Furtherm
ore, we show that smoothed versions of ($) over bar I-n,(X)(lambda) pr
ovide consistent estimates for the normalised transfer function for an
y p epsilon (0, 2] independent of p.