scholarly journals The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model

Bernoulli ◽  
2018 ◽  
Vol 24 (2) ◽  
pp. 1351-1393 ◽  
Author(s):  
Anja Janssen ◽  
Thomas Mikosch ◽  
Mohsen Rezapour ◽  
Xiaolei Xie
Keyword(s):  
Stochastic Volatility ◽  
Covariance Matrix ◽  
Stochastic Volatility Model ◽  
Sample Covariance Matrix ◽  
Sample Covariance ◽  
Volatility Model ◽  
Heavy Tailed

scholarly journals A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 689
Author(s):  
Łukasz Lenart ◽  
Anna Pajor ◽  
Łukasz Kwiatkowski
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Financial Time Series ◽  
Stochastic Volatility Model ◽  
Mcmc Methods ◽  
Statistical Framework ◽  
Typical Data ◽  
Volatility Model ◽  
Density Forecasting ◽  
Heavy Tailed

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian
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