Asymptotic spectral properties and extreme eigenvalues of sample correlation matrices from nonstationary high-dimensional VAR processes
Year: 2026
Type: preprint
Abstract: We study the limiting spectral distribution and extreme eigenvalues of the sample correlation matrix $\hat{\boldsymbol{R}}$ from a high-dimensional vector autoregressive (VAR) processes. Depending on whether roots of the characteristic polynomial of given VAR lie on (nonstationary) or outside (super-nonstationary) the unit circle, $\hat{\boldsymbol{R}}$ presents different types of asymptotic spectral properties. Under both nonstationary and super-nonstationary regimes, the empirical spectral distribution of $\hat{\boldsymbol{R}}$ degenerates in probability to a point mass at zero. The rescaled extreme eigenvalues of $\hat{\boldsymbol{R}}$ are asymptotically equivalent to the eigenvalues of a finite-dimensional symmetric random matrix determined by the characteristic roots. Moreover, under super-nonstationarity, $\hat{\boldsymbol{R}}$ degenerates in probability to a matrix with finite rank.
Source: arXiv (Cornell University)
Authors: Liu, Ruihan, Wang, Chen
Institution: University of Hong Kong
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223693004