Asymptotic results for long memory LARCH sequences

Berkes, István; Horváth, Lajos

Ann. Appl. Probab., Tome 13 (2003) no. 1, p. 641-668 / Harvested from Project Euclid

Résumé

For a LARCH ("linear ARCH") sequence $ (y_n, \sigma_n) $ exhibiting long range dependence, we determine the limiting distribution of sums $\sum f(y_n)$, $ \sum f(\sigma_n) $ for smooth functions $ f $ satisfying $E(y_0 f' (y_0)) \neq 0 $, $ E (\sigma_0 f' (\sigma_0)) \neq 0 $. We also give an approximation formula for the above sums, providing the first term of the asymptotic expansions of $ \sum f (y_n),\break \sum f (\sigma_n)$.

Publié le : 2003-05-14
Classification: LARCH sequences, long range dependence, asymptotic distribution, fractional Brownian motion, 60F17, 60K99

@article{1050689598,
     author = {Berkes, Istv\'an and Horv\'ath, Lajos},
     title = {Asymptotic results for long memory LARCH sequences},
     journal = {Ann. Appl. Probab.},
     volume = {13},
     number = {1},
     year = {2003},
     pages = { 641-668},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050689598}
}

Berkes, István; Horváth, Lajos. Asymptotic results for long memory LARCH sequences. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp.  641-668. http://gdmltest.u-ga.fr/item/1050689598/