We consider a simple stationary bilinear model $X_t = cX_{t-1}
Z_{t-1} + Z_t, t = 0, \pm 1, \pm 2, \dots,$ generated by heavy-tailed noise
variables ${Z_t}$. A complete analysis of weak limit behavior is given by means
of a point process analysis. A striking feature of this analysis is that the
sample correlation converges in distribution to a nondegenerate limit. A
warning is sounded about trying to detect nonlinearities in heavy-tailed models
by means of the sample correlation function.
Publié le : 1996-11-14
Classification:
Extreme value theory,
Poisson processes,
bilinear and nonlinear processes,
stable laws,
point processes,
stationary processes,
sample correlation,
60E07,
60F17,
60G55,
60G70,
62M10
@article{1035463328,
author = {Davis, Richard A. and Resnick, Sidney I.},
title = {Limit theory for bilinear processes with heavy-tailed
noise},
journal = {Ann. Appl. Probab.},
volume = {6},
number = {1},
year = {1996},
pages = { 1191-1210},
language = {en},
url = {http://dml.mathdoc.fr/item/1035463328}
}
Davis, Richard A.; Resnick, Sidney I. Limit theory for bilinear processes with heavy-tailed
noise. Ann. Appl. Probab., Tome 6 (1996) no. 1, pp. 1191-1210. http://gdmltest.u-ga.fr/item/1035463328/