We study long strange intervals in a linear stationary stochastic
process with regularly varying tails. It turns out that the length of the
longest strange interval grows, as a function of the sample size, at different
rates in different parts of the parameter space.We argue that this phenomenon
may be viewed in a fruitful way as a phase transition between short-and
long-range dependence.We prove a limit theorem that may form a basis for
statistical detection of long-range dependence.
Publié le : 2001-08-14
Classification:
Long-range dependence,
stationary process,
large deviations,
heavy tails,
infinite moving average,
maxima,
regular variation,
extreme value distribution,
applications in finance,
insurance,
telecommunications,
60G10,
60F15,
60G70
@article{1015345352,
author = {Mansfield, Peter and Rachev, Svetlozar T. and Samorodnitsky, Gennady},
title = {Long strange segments of a stochastic process},
journal = {Ann. Appl. Probab.},
volume = {11},
number = {2},
year = {2001},
pages = { 878-921},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345352}
}
Mansfield, Peter; Rachev, Svetlozar T.; Samorodnitsky, Gennady. Long strange segments of a stochastic process. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp. 878-921. http://gdmltest.u-ga.fr/item/1015345352/