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Explicit representation of finite predictor coefficients and its applications

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83799

Title: Explicit representation of finite predictor coefficients and its applications
Authors: Inoue, Akihiko Browse this author
Kasahara, Yukio Browse this author
Keywords: Predictior coefficients
AR coefficients
MA coefficients
prediction
fractional ARIMA processes
long memory
Baxter’s inequality
partial autocorrelation functions.
Issue Date: 2004
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 646
Start Page: 1
End Page: 32
Abstract: 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 involves the alternate iteration of projection operators associated with the infinite past and the infinite future. We provide several applications, which include rates of convergence of the finite predictor coefficients, an equality of Baxter-type for long memory processes, and a simple representation of the partial autocorrelation function α(·). We use the last result to obtain the precise asymptotic behavior of α(·) with remainder, for the fractional ARIMA processes.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69453
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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