| Project/Area Number |
12640148
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
INOUE Akihiko Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (50168431)
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| Co-Investigator(Kenkyū-buntansha) |
MAEJIMA Makoto Keio Univ., Faculty of Sci. and Tech., Prof., 理工学部, 教授 (90051846)
MIKAMI Toshio Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (70229657)
ARAI Asao Hokkaido Univ,. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (80134807)
KASAHARA Yuji Ochanomizu Univ., Faculty of Sci., Prof., 理学部, 教授 (60108975)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2001: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2000: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | Mercerian theorem / Tauberian theorem / partial autocorrelation function / FARIMA process / prediction theory / long memory / risky asset model / past and future method / 定常過程 / long memory |
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| Research Abstract |
Inoue and Bingham developed the theory of ratio Mercerian theorems introduced by themselves. In particular, they showed that ratio Mercerian theorems for systems can be used to prove various Tauberian theorems. For example, they proved Tauberian theorems for general kernels in the boundary case using that theory. They also proved Tauberian and Mercerian theorems for some arithmetic sums using this technique.
Inoue proved a representation theorem for partial autocorrelation functions of stationary time series, using the past and future method introduced by himself. Using the representation theorem, he determined the asymptotics for the partial autocorrelation functions of FARIMA processes, which are popular paremetric long-memory models.
Inoue and Anh introduced a dynamic model of risky asset prices with memory. They developed a theory for the model. In particular, they gave option pricing formulas in the financial market model with this risky asset.
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