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arXiv · 1211.5902

Eigenvalues of sample covariance matrices of non-linear processes with infinite variance

Richard A. Davis·Oliver Pfaffel
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Abstract

We study the $k$-largest eigenvalues of heavy-tailed sample covariance matrices of the form $\bX\bX^\T$ in an asymptotic framework, where the dimension of the data and the sample size tend to infinity. To this end, we assume that the rows of $\bX$ are given by independent copies of some stationary process with regularly varying marginals with index $\alpha\in(0,2)$ satisfying large deviation and mixing conditions. We apply these general results to stochastic volatility and GARCH processes.

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Richard A. Davis, Oliver Pfaffel. 2012-11-26. Eigenvalues of sample covariance matrices of non-linear processes with infinite variance. https://arxiv.org/abs/1211.5902

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