For the stable moving average process $$X^t =
\int_{-\infty}^{\infty} f(t + x)M(dx), t = 1, 2,\dots,$$ we find the weak limit
of its sample autocorrelation function as the sample size n increases to
$\infty$. It turns out that, as a rule, this limit is random! This shows how
dangerous it is to rely on sample correlation as a model fitting tool in the
heavy tailed case. We discuss for what functions f this limit is
nonrandom for all (or only some--this can be the case, too!) lags.
Publié le : 1999-08-14
Classification:
Heavy tails,
sample correlation,
acf,
stable process,
ARMA processes,
infinite variance,
moving average,
62M10,
60E07,
60G70
@article{1029962814,
author = {Resnick, Sidney and Samorodnitsky, Gennady and Xue, Fang},
title = {How misleading can sample ACFs of stable MAs be? (Very!)},
journal = {Ann. Appl. Probab.},
volume = {9},
number = {1},
year = {1999},
pages = { 797-817},
language = {en},
url = {http://dml.mathdoc.fr/item/1029962814}
}
Resnick, Sidney; Samorodnitsky, Gennady; Xue, Fang. How misleading can sample ACFs of stable MAs be? (Very!). Ann. Appl. Probab., Tome 9 (1999) no. 1, pp. 797-817. http://gdmltest.u-ga.fr/item/1029962814/