论文标题
线性过程的大型样品自动助矩阵，带有沉重的尾巴
Large sample autocovariance matrices of linear processes with heavy tails
论文作者
论文摘要
我们为具有无限第四刻的高维时间序列的样品自相关矩阵的某些功能提供了渐近理论。时间序列表现出跨坐标和时间的线性依赖性。假设尺寸随样本量的增加而增加，我们为样本自动助矩阵的特征向量提供了理论，并找到了简单结构的明确近似值，该结构的有限样本质量被说明用于模拟数据。我们还获得了样品自相关矩阵功能的归一化特征值的限制。反过来，我们得出了作用于它们的最大特征值及其功能的分布限制。在我们的证明中，我们使用大型偏差技术来进行重尾过程，点过程技术是由极值理论激励的，以及相关的连续映射论点。
We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time. Assuming that the dimension increases with the sample size, we provide theory for the eigenvectors of the sample autocovariance matrices and find explicit approximations of a simple structure, whose finite sample quality is illustrated for simulated data. We also obtain the limits of the normalized eigenvalues of functions of the sample autocovariance matrices in terms of cluster Poisson point processes. In turn, we derive the distributional limits of the largest eigenvalues and functionals acting on them. In our proofs, we use large deviation techniques for heavy-tailed processes, point process techniques motivated by extreme value theory, and related continuous mapping arguments.
