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The eigenstructure of the sample covariance matrices of high-dimensional stochastic volatility models with heavy tails. (English) Zbl 1430.62195

A high-dimensional stochastic volatility time series is considered for the case when dimension grows with the sample size. The authors focuse on analysis of the dependence structure of observations from time series based on the spectral properties of the sample covariance matrix. Both the stationary case, i.e. the marginal distribution does not change over time, and the nonstationary case of an iid stochastic volatility field with time-varying marginal distribution are considered. The main results of this paper concern convergence results for the stochastic volatility model.

MSC:

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