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Seminar on Probability and Statistics
Seminar information archive ～11/11｜Next seminar｜Future seminars 11/12～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
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Future seminars
2025/11/12
10:30-11:40 Room #126 (Graduate School of Math. Sci. Bldg.)
Lars Winkelmann (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
Lars Winkelmann (Free University of Berlin)
Testing the Maximal Rank of Time-Varying Covariance Matrices in Noisy High-Frequency Data (English)
[ Abstract ]
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.
[ Reference 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
