2017 Fiscal Year Final Research Report
Statistical inference for stochastic differential equations and its applications to high frequency data analysis
| Project/Area Number |
24300107
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
吉田 朋広 東京大学, 大学院数理科学研究科, 教授 (90210707)
増田 弘毅 九州大学, 数理学研究院, 教授 (10380669)
深澤 正彰 大阪大学, 学内共同利用施設等, その他 (70506451)
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| Project Period (FY) |
2012-04-01 – 2018-03-31
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| Keywords | 数理統計学 / 拡散過程 / Levy過程駆動型SDE / 疑似尤度解析 / 高頻度不規則観測 / セミマルチンゲール / 非整数ブラウン運動 / ボラティリティ |
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| Outline of Final Research Achievements |
We considered sampling problems for diffusion type processes. For parametric inference of stochastic differential equations based on high frequency data, it is important to obtain a quasi-maximum likelihood estimator (QMLE). In order to compute the QMLE efficiently, we proposed the hybrid type estimator by using advantages of both Bayes type estimation and the maximum likelihood type estimation. Moreover, the mathematical validity of the proposed estimator was shown and we confirmed that the proposed estimator had good performance by large scale numerical simulations. The proposed statistical method works well for not only diffusion type models including ergodic diffusions and small diffusions but general models. We also researched statistical inference for Levy driven stochastic differential equations and applications of statistical inference for stochastic differential equations to high frequency data analysis.
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| Free Research Field |
統計科学
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