On spectral distribution of high dimensional covariation matrices

Claudio Heinrich; Mark Podolskij

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arXiv · 1410.6764

On spectral distribution of high dimensional covariation matrices

Claudio Heinrich·Mark Podolskij

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Abstract

In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider $N$-dimensional Ito integrals with time varying matrix-valued integrands. We observe $n$ equidistant high frequency data points of the underlying Brownian diffusion and we assume that $N/n\rightarrow c\in (0,\infty)$. We show that under a certain mixed spectral moment condition the spectral distribution of the empirical covariation matrix converges in distribution almost surely. Our proof relies on method of moments and applications of graph theory.

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Claudio Heinrich, Mark Podolskij. 2014-10-24. On spectral distribution of high dimensional covariation matrices. https://arxiv.org/abs/1410.6764

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