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Hokkaido University Preprint Series in Mathematics >
Applications of a finite-dimensional duality principle to some prediction problems
| Title: | Applications of a finite-dimensional duality principle to some prediction problems |
| Authors: | Kasahara, Yukio Browse this author | | Pourahmadi, Mohsen Browse this author | | Inoue, Akihiko Browse this author |
| Keywords: | Finite prediction problems | | biorthogonality and duality | | missing values | | stationary time series | | Wold decomposition |
| Issue Date: | 2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 871 |
| Start Page: | 1 |
| End Page: | 15 |
| Abstract: | Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in Hilbert spaces of analytic functions (Nakazi, 1984) to linear regression in statistics (Box and Tiao, 1975). We unify these results via a finite-dimensional duality lemma and elementary ideas from the linear algebra. The approach reveals the inherent finite-dimensional character of many difficult prediction problems, the role of duality and biorthogonality for a finite set of random variables. The lemma is particularly useful when the number of missing values is small, like one or two, as in the case of Kolmogorov and Nakazi prediction problems. The stationarity of the underlying process is not a requirement. It opens up the possibility of extending such results to nonstationary processes. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69680 |
| 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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