State space modeling of long-memory processes

• 成果类型: Article
• 署名作者: Chan, NH; Palma, W
• 署名单位: Carnegie Mellon University; Pontificia Universidad Catolica de Chile
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 719-740
• 关键词: time-series models

摘要

This paper develops a state space modeling for long-range dependent data. Although a long-range dependent process has an infinite-dimensional state space representation, it is shown that by using the Kalman filter, the exact likelihood function can be computed recursively in a finite number of steps. Furthermore, an approximation to the likelihood function based on the truncated state space equation is considered. Asymptotic properties of these approximate maximum likelihood estimates are established for a class of long-range dependent models, namely, the fractional autoregressive moving average models. Simulation studies show rapid converging properties of the approximate maximum likelihood approach.