标题： 基于张量因子结构的大波动矩阵预测 显示英文标题

标题： Large Volatility Matrix Prediction using Tensor Factor Structure

摘要： 已开发出几种基于高维因子驱动的伊藤过程来预测大波动矩阵的方法。 这些方法通常会施加限制以降低模型复杂性，比如时间上恒定的特征向量或因子载荷。 然而，一些研究表明特征向量过程也是随时间变化的。 为了解决这一特性，本文通过将整合波动率矩阵过程表示为立方（三阶张量）形式来推广因子结构，该形式被分解为低秩张量和特异张量成分。 为了预测条件期望的大波动矩阵，我们提出了投影张量主正交成分阈值（PT-POET）程序，并建立了其渐近性质。 PT-POET的优势通过模拟研究得到验证，并在一个使用高频交易数据的最小方差投资组合分配应用中得以展示。 显示英文摘要

摘要： Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based It\^o processes. These methods often impose restrictions to reduce the model complexity, such as constant eigenvectors or factor loadings over time. However, several studies indicate that eigenvector processes are also time-varying. To address this feature, this paper generalizes the factor structure by representing the integrated volatility matrix process as a cubic (order-3 tensor) form, which is decomposed into low-rank tensor and idiosyncratic tensor components. To predict conditional expected large volatility matrices, we propose the Projected Tensor Principal Orthogonal componEnt Thresholding (PT-POET) procedure and establish its asymptotic properties. The advantages of PT-POET are validated through a simulation study and demonstrated in an application to minimum variance portfolio allocation using high-frequency trading data.