Matrix-based Prediction Approach for Intraday Instantaneous Volatility Vector

In this article, we introduce a novel method for predicting intraday instantaneous volatility based on Itô semimartingale models using high-frequency financial data. Several studies have highlighted stylized volatility time series features, such as interday auto-regressive dynamics and the intraday U-shaped pattern. To accommodate these volatility features, we propose an interday-by-intraday instantaneous volatility matrix process that can be decomposed into low-rank conditional expected instantaneous volatility and noise matrices. To predict the low-rank conditional expected instantaneous volatility matrix, we propose the Two-sIde Projected-PCA (TIP-PCA) procedure. We establish asymptotic properties of the proposed estimators and conduct a simulation study to assess the finite sample performance of the proposed prediction method. Finally, we apply the TIP-PCA method to an out-of-sample instantaneous volatility vector prediction study using high-frequency data from the S&P 500 index and 11 sector index funds.

本文提出一种基于伊藤半鞅（Itô semimartingale）模型、利用高频金融数据预测日内瞬时波动率的全新方法。已有多项研究揭示了波动率时序的典型事实特征，诸如日间自回归动态与日内U型分布模式。为适配上述波动率特征，我们构建了日间-日内联合瞬时波动率矩阵过程，该过程可分解为低秩条件期望瞬时波动率矩阵与噪声矩阵。针对低秩条件期望瞬时波动率矩阵的预测任务，我们提出双侧投影主成分分析（Two-sIde Projected-PCA，TIP-PCA）方法。本文论证了所提估计量的渐近性质，并通过仿真实验评估了所提预测方法的有限样本表现。最后，我们利用标普500（S&P 500）指数与11只行业指数基金的高频金融数据，将TIP-PCA方法应用于样本外瞬时波动率向量预测研究。