Various parametric models have been developed to predict large volatility matrices, based on the approximate factor model structure. They mainly focus on the dynamics of the factor volatility with some finite high-order moment assumptions. However, the empirical studies have shown that the idiosyncratic volatility also has a dynamic structure and it comprises a large proportion of the total volatility. Furthermore, we often observe that the financial market exhibits heavy tails. To account for these stylized features in financial returns, we introduce 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. To handle the heavy-tailedness and curse of dimensionality, we propose a robust parameter estimation method for a high-dimensional VAR model. We apply the robust estimator to predicting large volatility matrices and investigate its asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed estimation and prediction methods. Using high-frequency trading data, we apply the proposed method to large volatility matrix prediction and minimum variance portfolio allocation and showcase the new model and the proposed method.
翻译:开发了各种参数模型,以预测基于大致要素模型结构的大型波动矩阵,主要侧重于因子波动的动态动态,有一定的高度瞬间假设,但实证研究表明,特异性波动也具有动态结构,它占总波动的很大比例。此外,我们经常观察到金融市场的尾巴很重。为了说明金融回报中的这些结构化特点,我们为因子和特异性综合挥发性引入了一个新型的It ⁇ o}扩散过程,其值随矢量自动递增模式而增加。我们称之为因子和特异性VAR-It ⁇ o}(FIVAR-It ⁇ o)模型。为了处理重尾尾尾部和对维度的诅咒,我们为高维度VAR模型提出了一种强的参数估计方法。我们运用了强有力的估计方法来预测大型波动矩阵,并调查其是否具有湿度特性。我们进行了模拟研究,以验证拟议的大规模交易模型性VAR-Itro)模型业绩,并采用拟议的最低变异性预测方法。