HAR-Ito models and high-dimensional HAR modeling for high-frequency data
HAR–Itô 模型与高频数据的高维 HAR 建模AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要围绕高频金融数据的已实现波动率、HAR 模型及其高频随机动态展开。
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HAR–Itô 模型与高频数据的高维 HAR 建模
- 研究问题
- 如何使已实现波动率的 HAR 模型灵活选择异质成分，解释对应的高频随机动态，并支持多资产场景中的高维估计分析？
- 方法与思路
- 作者利用张量技术构造多线性低秩 HAR 模型，数据驱动选择异质成分，并引入 HAR–Itô 模型与投影梯度下降估计算法。
- 材料陈述的贡献
- 摘要称建立了高维建模的非渐近性质和算法理论依据，给出 HAR 类模型的高频动态解释，并以模拟及真实数据展示方法。
- 阅读关注点
- 应核对张量低秩约束、异质成分选择规则、连续时间与离散模型的对应关系，以及非渐近界和算法保证依赖的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未给出误差界、收敛条件或实证数值，无法判断优势的适用范围。
原文摘要
It is an important task to model realized volatilities for high-frequency data in finance and economics and, as arguably the most popular model, the heterogeneous autoregressive (HAR) model has dominated the applications in this area. However, this model suffers from three drawbacks: (i.) its heterogeneous volatility components are linear combinations of daily realized volatilities with fixed weights, which limit its flexibility for different types of assets, (ii.) it is still unknown what is the high-frequency probabilistic structure for this model, as well as many other HAR-type models in the literature, and (iii.) there is no high-dimensional inference tool for HAR modeling although it is common to encounter many assets in real applications. To overcome these drawbacks, this paper proposes a multilinear low-rank HAR model by using tensor techniques, where a data-driven method is adopted to automatically select the heterogeneous components. In addition, HAR-Itô models are introduced to interpret the corresponding high-frequency dynamics, as well as those of other HAR-type models. Moreover, non-asymptotic properties of the high-dimensional HAR modeling are established, and a projected gradient descent algorithm with theoretical justifications is suggested to search for estimates. Theoretical and computational properties of the proposed method are verified by simulation studies, and the necessity of using the data-driven method for heterogeneous components is illustrated in real data analysis.