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Explicit representation of finite predictor coefficients and its applications
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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