Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2026-08-28
Number: 26-060/III
Author-Name: Justus Holman
Author-Workplace-Name: Vrije Universiteit Amsterdam 
Author-Name: Yicong Lin
Author-Workplace-Name: Vrije Universiteit Amsterdam 
Author-Name: Andre Lucas
Author-Workplace-Name: Vrije Universiteit Amsterdam 
Author-Name: Anne Opschoor
Author-Workplace-Name: Vrije Universiteit Amsterdam 
Title: Joint Eigenvector and Eigenvalue Dynamics with an Application to Time-Varying Covariance Matrices
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.
Classification-JEL: C32, C53, C58
Keywords: 
File-URL: https://papers.tinbergen.nl/26060.pdf
File-Format: application/pdf
File-Size: 7.456.848 bytes
Handle: RePEc:tin:wpaper:20260060