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arXiv · 2310.06073

Spectral norm bounds for high-dimensional realized covariance matrices and application to weak factor models

Yuta Koike
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Abstract

Motivated by statistical analysis of latent factor models for high-frequency financial data, we develop sharp upper bounds for the spectral norm of the realized covariance matrix of a high-dimensional It\^o semimartingale with possibly infinite activity jumps. For this purpose, we develop Burkholder-Gundy type inequalities for matrix martingales with the help of the theory of non-commutative $L^p$ spaces. The obtained bounds are applied to estimating the number of (relevant) common factors in a continuous-time latent factor model from high-frequency data in the presence of weak factors.

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Yuta Koike. 2023-10-09. Spectral norm bounds for high-dimensional realized covariance matrices and application to weak factor models. https://arxiv.org/abs/2310.06073

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