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統計数学セミナー
過去の記録 ～10/30｜次回の予定｜今後の予定 10/31～
| 担当者 | 吉田朋広、増田弘毅、荻原哲平、小池祐太 |
|---|---|
| 目的 | 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う. |
次回の予定
2025年11月12日(水)
10:30-11:40 数理科学研究科棟(駒場) 126号室
ハイブリッド開催
Lars Winkelmann 氏 (Free University of Berlin)
Testing the Maximal Rank of Time-Varying Covariance Matrices in Noisy High-Frequency Data (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/eRqQutp7TTeKmqH2Vhm8Xg
ハイブリッド開催
Lars Winkelmann 氏 (Free University of Berlin)
Testing the Maximal Rank of Time-Varying Covariance Matrices in Noisy High-Frequency Data (English)
[ 講演概要 ]
We address the problem of testing the maximal rank of time-varying covariance matrices in high-frequency diffusion models observed with additive noise. Building on a spectral representation of the quadratic covariation operator, we construct test statistics based on empirical eigenvalues of localized spectral covariance matrices. The presence of observational noise and the rotation of the eigenspace introduce a fundamental bias-variance trade-off. We derive the optimal separation rate at which the tests retain power, showing its dependence on both the smoothness of the covariance process and the existence of a spectral gap. Our theoretical framework integrates matrix perturbation theory, concentration inequalities, and statistical lower bound approaches. Simulations illustrate the performance of our methods, and an application to portfolios of government bonds underscores their practical relevance in financial econometrics.
[ 参考URL ]We address the problem of testing the maximal rank of time-varying covariance matrices in high-frequency diffusion models observed with additive noise. Building on a spectral representation of the quadratic covariation operator, we construct test statistics based on empirical eigenvalues of localized spectral covariance matrices. The presence of observational noise and the rotation of the eigenspace introduce a fundamental bias-variance trade-off. We derive the optimal separation rate at which the tests retain power, showing its dependence on both the smoothness of the covariance process and the existence of a spectral gap. Our theoretical framework integrates matrix perturbation theory, concentration inequalities, and statistical lower bound approaches. Simulations illustrate the performance of our methods, and an application to portfolios of government bonds underscores their practical relevance in financial econometrics.
https://u-tokyo-ac-jp.zoom.us/meeting/register/eRqQutp7TTeKmqH2Vhm8Xg
