The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model
The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model
复制标题
多元重尾随机波动率模型样本协方差矩阵的特征值
DOI：
10.3150/16-bej901
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Xiao
中科院分区：
文献类型：
--
作者：
Anja Janssen;T. Mikosch;M. Rezapour;Xiao
考虑了一个多变量重尾随机波动率模型，分析了其样本协方差矩阵的大样本行为。我们研究了它的条目在无限方差的情况下的极限行为，并得出结果的有序特征值和相应的特征向量。从本质上讲，我们考虑两种不同的情况下，尾部行为要么源于i.i.d.。创新的过程或从其挥发序列。在这两种情况下，我们利用一个大偏差技术，经常变化的时间序列，以获得多变量\alpha\稳定的极限分布的样本协方差矩阵。虽然我们表明，在重尾创新的情况下的限制行为类似于完全独立的观察，我们还得出，在重尾波动率序列的情况下，可能的限制行为是更多样化的，即允许依赖性的限制分布，这是由潜在的波动率序列的结构。
We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for the ordered eigenvalues and corresponding eigenvectors. Essentially, we consider two different cases where the tail behavior either stems from the i.i.d. innovations of the process or from its volatility sequence. In both cases, we make use of a large deviations technique for regularly varying time series to derive multivariate $\alpha$-stable limit distributions of the sample covariance matrix. While we show that in the case of heavy-tailed innovations the limiting behavior resembles that of completely independent observations, we also derive that in the case of a heavy-tailed volatility sequence the possible limiting behavior is more diverse, i.e. allowing for dependencies in the limiting distributions which are determined by the structure of the underlying volatility sequence.
影响因子：
1.5
作者：
Janssen, Anja;Drees, Holger
通讯作者：
Drees, Holger