The eigenstructure of the sample covariance matrices of high-dimensional stochastic volatility models with heavy tails

DOI10.3150/18-BEJ1103zbMath1430.62195arXiv2001.04964OpenAlexW2975762410MaRDI QIDQ2325386

Thomas Mikosch, Johannes Heiny

Publication date: 25 September 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.04964

zbMATH Keywords

convergenceregular variationtracepoint processlarge deviationsdependent entriesFréchet distributioninfinite variance stable limitlargest eigenvaluessample autocovariance matrixcluster Poisson limit

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Applications of statistics to actuarial sciences and financial mathematics (62P05) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (6)

Eigenvector statistics of Lévy matrices ⋮ High-dimensional sample covariance matrices with Curie-Weiss entries ⋮ Asymptotic behavior of eigenvalues of variance-covariance matrix of a high-dimensional heavy-tailed Lévy process ⋮ Extreme eigenvalue statistics of \(m\)-dependent heavy-tailed matrices ⋮ The asymptotic distribution of the condition number for random circulant matrices ⋮ Limiting distributions for eigenvalues of sample correlation matrices from heavy-tailed populations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extreme eigenvalues of sparse, heavy tailed random matrices
• A large deviations approach to limit theory for heavy-tailed time series
• Precise large deviations for dependent regularly varying sequences
• Extreme value analysis for the sample autocovariance matrices of heavy-tailed multivariate time series
• Poisson convergence for the largest eigenvalues of heavy tailed random matrices
• Limiting behavior of the eigenvalues of a multivariate F matrix
• Spectral analysis of large dimensional random matrices
• The limiting empirical measure of multiple discriminant ratios
• Estimation and asymptotic covariance matrix for stochastic volatility models
• Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails
• Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices with general growth rates: the iid case
• The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model
• Stochastic volatility models with possible extremal clustering
• Random matrix theory in statistics: a review
• Stochastic Models with Power-Law Tails
• Least tail-trimmed squares for infinite variance autoregressions
• Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
• Point process convergence of stochastic volatility processes with application to sample autocorrelation
• Handbook of Financial Time Series
• Stochastic Volatility: Origins and Overview
• Equilibrium excess-of-loss reinsurance–investment strategy for a mean–variance insurer under stochastic volatility model
• Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
• PORTFOLIO OPTIMIZATION AND STOCHASTIC VOLATILITY ASYMPTOTICS
• Self-Weighted Least Absolute Deviation Estimation for Infinite Variance Autoregressive Models
• Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model
• Handbook of Volatility Models and Their Applications
• Heavy-Tail Phenomena
• Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series

This page was built for publication: The eigenstructure of the sample covariance matrices of high-dimensional stochastic volatility models with heavy tails