Open Access
May 2003 Asymptotic results for long memory LARCH sequences
István Berkes, Lajos Horváth
Ann. Appl. Probab. 13(2): 641-668 (May 2003). DOI: 10.1214/aoap/1050689598


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)$.


Download Citation

István Berkes. Lajos Horváth. "Asymptotic results for long memory LARCH sequences." Ann. Appl. Probab. 13 (2) 641 - 668, May 2003.


Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1032.62078
MathSciNet: MR1970281
Digital Object Identifier: 10.1214/aoap/1050689598

Primary: 60F17
Secondary: 60K99

Keywords: asymptotic distribution , fractional Brownian motion , LARCH sequences , Long range dependence

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.13 • No. 2 • May 2003
Back to Top