Department of Economics and Business Economics

On spectral distribution of high dimensional covariation matrices

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  • rp14_54

    Submitted manuscript, 551 KB, PDF document

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 Itô 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 -> c in (0,oo). 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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages20
Publication statusPublished - 15 Dec 2014
SeriesCREATES Research Papers
Number2014-54

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