2022 Fiscal Year Final Research Report
Statistical Hypothesis Testing for Roughness of Volatility
| Project/Area Number |
19K23224
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0107:Economics, business administration, and related fields
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2019-08-30 – 2023-03-31
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| Keywords | 非整数Brown運動 / 高頻度観測 / 観測誤差 / 確率ボラティリティ |
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| Outline of Final Research Achievements |
In order to accurately estimate the Hurst index and volatility of the driving noise of the log-volatility process, which is a latent variable, from the log-realized variance time series data, we developed a theory of estimating the Hurst index and volatility of the driving noise under noisy observations. In this study, we analyze the local asymptotic behavior of the likelihood ratio random fields under the condition that high-frequently observed data of the fractional Brownian motion contains observational errors, so that we succeeded to derive optimal convergence rates and asymptotic variances of estimators and construct an estimator that satisfies the asymptotic optimality.
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| Free Research Field |
数理統計学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究で行なった高頻度観測データからスケール則や観測誤差の構造を推定する手法の開発、特に最適な収束レートや漸近分散を満たす推定量の開発は幾つかの技術的困難によりこれまで未解決な問題であったため、本研究の学術的意義は大きいと考える。また上述したファイナンスの問題に限らず、計量経済学や工学などの分野で観測される実際のデータには、推定したい確率過程とは別の確率過程が観測誤差として含まれる状況がごく自然に生じるため、様々な分野への応用が今後期待できる。
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