Statistical theory for the analysis of long-memory financial time series using continuous-time models
| Project/Area Number |
24530224
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Economic statistics
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| Research Institution | Gakushuin University (2013-2015)
Hitotsubashi University (2012) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 連続時間確率過程 / Hurst パラメータ / 最尤推定量 / フラクショナル・モデル / エルゴード的な場合 / 非エルゴード的な場合 / 特性関数 / 数値積分 / Fractional O-U process / 非エルゴード性 / ギルサノフの定理 / 極限分布 / フラクショナル O-U モデル / ergodic case / フラクショナル・ブラウン運動 / 確率過程 / O-U 過程 / フラクショナル・Brown 運動 |
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| Outline of Final Research Achievements |
We investigated the estimation problem for the drift parameter α in the fO-U (fractional Ornstein-Uhlenbeck) process which is a long-memory continuous-time stochastic process.Numerical integration was employed to compute the probability density of the MLE and the density was graphically presented. Asymptotic theory was also developed as the time span goes to infinity. It was proved that the MLE for the non-ergodic case converges to Cauchy distribution. The distribution depends on the Hurst parameter H and is symmetric around H=1/2. It was aslo proved that the concentration probability increases as H gets away from 1/2. These results were published in international refereed journals.
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Report
(5 results)
Research Products
(14 results)
