This paper introduces a novel It\^{o} diffusion process for both factor and idiosyncratic volatilities whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR-It\^{o} (FIVAR-It\^o) model. The FIVAR-It\^o model considers dynamics of the factor and idiosyncratic volatilities and involve many parameters. In addition, the empirical studies have shown that the financial returns often exhibit heavy tails. To address these two issues simultaneously, we propose a penalized optimization procedure with a truncation scheme for a parameter estimation. We apply the proposed parameter estimation procedure to predicting large volatility matrices and investigate its asymptotic properties. Using high-frequency trading data, the proposed method is applied to large volatility matrix prediction and minimum variance portfolio allocation.

翻译：本文提出了一种新颖的Itô扩散过程，用于描述因子波动率与特质波动率，其特征值服从向量自回归（VAR）模型。我们称之为因子与特质VAR-Itô（FIVAR-Itô）模型。该模型考虑了因子与特质波动率的动态变化，涉及大量参数。此外，实证研究表明金融收益率常呈现重尾特征。为同时解决这两个问题，我们提出了一种基于截断方案的惩罚优化参数估计方法。我们将所提参数估计方法应用于大维波动率矩阵预测，并探究其渐近性质。基于高频交易数据，该方法被应用于大维波动率矩阵预测与最小方差投资组合配置。