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On spectral distribution of high dimensional covariation matrices

Publikation: Working paper/Preprint Working paperForskning

Standard

On spectral distribution of high dimensional covariation matrices. / Heinrich, Claudio; Podolskij, Mark.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2014.

Publikation: Working paper/Preprint Working paperForskning

Harvard

Heinrich, C & Podolskij, M 2014 'On spectral distribution of high dimensional covariation matrices' Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Heinrich, C., & Podolskij, M. (2014). On spectral distribution of high dimensional covariation matrices. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers Nr. 2014-54

CBE

Heinrich C, Podolskij M. 2014. On spectral distribution of high dimensional covariation matrices. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Heinrich, Claudio og Mark Podolskij On spectral distribution of high dimensional covariation matrices. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal nr. 2014-54). 2014., 20 s.

Vancouver

Heinrich C, Podolskij M. On spectral distribution of high dimensional covariation matrices. Aarhus: Institut for Økonomi, Aarhus Universitet. 2014 dec 15.

Author

Heinrich, Claudio ; Podolskij, Mark. / On spectral distribution of high dimensional covariation matrices. Aarhus : Institut for Økonomi, Aarhus Universitet, 2014. (CREATES Research Papers; Nr. 2014-54).

Bibtex

@techreport{e1400490894e4d7ba6696a9352d6e3b6,
title = "On spectral distribution of high dimensional covariation matrices",
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 It{\^o} 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 = " Random matrices, Diffusion processes, Graphs, High frequency data",
author = "Claudio Heinrich and Mark Podolskij",
year = "2014",
month = dec,
day = "15",
language = "English",
series = "CREATES Research Papers",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
number = "2014-54",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - On spectral distribution of high dimensional covariation matrices

AU - Heinrich, Claudio

AU - Podolskij, Mark

PY - 2014/12/15

Y1 - 2014/12/15

N2 - 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.

AB - 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.

KW - Random matrices

KW - Diffusion processes

KW - Graphs

KW - High frequency data

M3 - Working paper

T3 - CREATES Research Papers

BT - On spectral distribution of high dimensional covariation matrices

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -