Large sample behaviour of high dimensional autocovariance matrices

DOI10.1214/15-AOS1378zbMath1343.62053arXiv1603.09145MaRDI QIDQ282456

Monika Bhattacharjee, Arup Bose

Publication date: 12 May 2016

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09145

zbMATH Keywords

limiting spectral distributionfree cumulantsmoment method\(\ast\)-algebraasymptotically freecompound free PoissonID matrixinfinite dimensional vector linear processnon-commutative probability spacenon-crossing partitionssemi-circle lawStieltjes transformationsymmetrized autocovariance matricesWigner matrix

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Free probability and free operator algebras (46L54) Diagnostics, and linear inference and regression (62J20)

Related Items

Principal components in linear mixed models with general bulk ⋮ Large sample behaviour of high dimensional autocovariance matrices ⋮ Polynomial generalizations of the sample variance-covariance matrix when pn−1 → 0 ⋮ On the Spectrum of Sample Covariance Matrices for Time Series ⋮ On the asymptotic behavior of the eigenvalue distribution of block correlation matrices of high-dimensional time series ⋮ Smallest singular value and limit eigenvalue distribution of a class of non-Hermitian random matrices with statistical application ⋮ Spectral measure of empirical autocovariance matrices of high-dimensional Gaussian stationary processes ⋮ Singular value distribution of dense random matrices with block Markovian dependence ⋮ Unnamed Item ⋮ Matrix polynomial generalizations of the sample variance-covariance matrix when \(pn^{-1}\to y(0,\infty)\) ⋮ Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model ⋮ On testing for high-dimensional white noise ⋮ Joint convergence of sample autocovariance matrices when \(p/n\to 0\) with application ⋮ On the empirical spectral distribution for matrices with long memory and independent rows ⋮ High-dimensional linear models: a random matrix perspective ⋮ On the behavior of large empirical autocovariance matrices between the past and the future ⋮ Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large sample behaviour of high dimensional autocovariance matrices
• A note on a Marčenko-Pastur type theorem for time series
• Spectral analysis of large dimensional random matrices
• Chain enumeration and non-crossing partitions
• On the empirical distribution of eigenvalues of a class of large dimensional random matrices
• Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
• On the Marčenko-Pastur law for linear time series
• The generalized dynamic factor model consistency and rates
• Limiting spectral distribution of a symmetrized auto-cross covariance matrix
• ESTIMATION OF AUTOCOVARIANCE MATRICES FOR INFINITE DIMENSIONAL VECTOR LINEAR PROCESS
• TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS
• Lectures on the Combinatorics of Free Probability
• An Introduction to Random Matrices
• Eigenvalue distribution of large sample covariance matrices of linear processes
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• The Generalized Dynamic Factor Model

This page was built for publication: Large sample behaviour of high dimensional autocovariance matrices