SOME LIMIT THEORY FOR THE SELF-NORMALIZED PERIODOGRAM OF STABLE PROCESSES

Citation
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
Citations number
10
Categorie Soggetti
Statistic & Probability","Statistic & Probability
ISSN journal
03036898
Volume
21
Issue
4
Year of publication
1994
Pages
485 - 491
Database
ISI
SICI code
0303-6898(1994)21:4<485:SLTFTS>2.0.ZU;2-M
Abstract
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.