On spectral distribution of high dimensional covariation matrices

2014/10/24 by Heinrich, Claudio, Podolskij, Mark · 1 citation
#60F05 #60F17 #62E20 #62M07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1410.6764

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→ c∈ (0,∞). 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.

Cited by

• Spectral analysis of high-dimensional spot volatility matrix with applications

Related

• Weak convergence of the empirical spectral distribution of ultra-high-dimensional banded sample covariance matrices
• Eigenvectors of Sample Covariance Matrices: Universality of global fluctuations
• On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations
• Analysis of the limiting spectral distribution of large dimensional General information-plus-noise type matrices
• Properties of linear spectral statistics of frequency-smoothed estimated spectral coherence matrix of high-dimensional Gaussian time series