Joint Eigenvector and Eigenvalue Dynamics with an Application to Time-Varying Covariance Matrices

Justus Holman, Yicong Lin, Andre Lucas and Anne Opschoor
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Justus Holman: Vrije Universiteit Amsterdam
Yicong Lin: Vrije Universiteit Amsterdam
Andre Lucas: Vrije Universiteit Amsterdam
Anne Opschoor: Vrije Universiteit Amsterdam

No 26-060/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We introduce the Dynamic Spectral Rotation (DSR) model, allowing for dynamics in both eigenvalues and eigenvectors of time-varying conditional covariance matrices. The construction preserves orthonormality of the entire eigenvector matrix at every point in time. We study the model’s asymptotic properties and establish unique identification of all static parameters governing the joint dynamics of eigenvalues and eigenvectors. Notably, the parameters that determine the dynamic rotation angles remain uniquely identified under mild conditions even when the rotation angles are allowed to evolve over ranges far beyond intervals of length π. In an empirical application to US equity returns, we show that allowing the leading eigendirection of the covariance matrix to vary over time significantly improves the predicted portfolio covariance structure compared to a model in which all eigendirections are held fixed.

JEL-codes: C32 C53 C58 (search for similar items in EconPapers)
Date: 2026-08-28
New Economics Papers: this item is included in nep-ets and nep-inv
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