On spectral distribution of high dimensional covariation matrices

Claudio Heinrich () and Mark Podolskij ()
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Claudio Heinrich: Aarhus University, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark
Mark Podolskij: Aarhus University and CREATES, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 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.

Keywords: Diffusion processes; graphs; high frequency data; random matrices. (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 18
Date: 2014-12-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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