High-dimensional covariance matrices under dynamic volatility models: Asymptotics and shrinkage estimation

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Theoretical analysis reveals conditions altering spectral limits under dynamic volatility models, highlighting optimal nonlinear shrinkage.

A time-variation adjusted sample covariance matrix overcomes nonlinear dependencies, ensuring its limiting spectral distribution follows the classical Marčenko–Pastur law.
Theoretical derivation establishes the exact condition where limiting spectral distributions under scalar BEKK models deviate systematically from independent observations.
The asymptotic framework enables a consistent population spectrum estimator and an asymptotically optimal nonlinear shrinkage estimator for unconditional covariance matrices.

Ding et al. (2024) studied this question.

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Theoretical analysis reveals conditions altering spectral limits under dynamic volatility models, highlighting optimal nonlinear shrinkage.