Explicit representation of finite predictor coefficients and its applications

• 成果类型: Article
• 署名作者: Inoue, Akihiko; Kasahara, Yukio
• 署名单位: Hokkaido University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000209
• 发表日期: 2006
• 页码: 973-993
• 关键词: partial autocorrelation functions; fractional arima processes; STOCHASTIC-PROCESSES; interpolation

摘要

We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.