Asymptotic results for long memory LARCH sequences

• 成果类型: Article
• 署名作者: Berkes, I; Horváth, J
• 署名单位: HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Utah System of Higher Education; University of Utah
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 641-668
• 关键词: CENTRAL-LIMIT-THEOREM; Empirical Process; CONDITIONAL HETEROSCEDASTICITY; CONVERGENCE

摘要

For a LARCH (linear ARCH) sequence (Y-n, sigma(n),) exhibiting long range dependence, we determine the limiting distribution of sums Sigma f (y(n)), Sigma f (sigma(n)) for smooth functions f satisfying E(y(0)f' (y(0))) = 0, E (sigma(0)f' (sigma(0))) not equal 0. We also give an approximation formula for the above sums, providing the first term of the asymptotic expansions of Sigma f (y(n)), Sigma f (sigma(n)).