ASYMPTOTIC-DISTRIBUTION OF STATISTICS IN TIME-SERIES

• 成果类型: Article
• 署名作者: GOTZE, F; HIPP, C
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325772
• 发表日期: 1994
• 页码: 2062-2088
• 关键词: dependent random vectors; gaussian arma processes; expansions; sums; estimators

摘要

Verifiable conditions are given for the validity of formal Edgeworth expansions for the distribution of sums X(1) + ... + X(n), where X(i) = F(Z(i), ..., Z(i + p - 1)) and Z(1),Z(2), ... is a strict sense stationary sequence that can be written as Z(j) = g(epsilon(j-k): k greater than or equal to 0) with an lid sequence (epsilon(i)) of innovations. These models include nonlinear functions of ARMA processes (Z(i)) as well as certain nonlinear AR processes. The results apply to many statistics in (nonlinear) time series models.