On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations
基于含噪高频观测的高维协方差矩阵谱分布推断AI 解读 ↓
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基于含噪高频观测的高维协方差矩阵谱分布推断
- 研究问题
- 在高维高频观测受到微观结构噪声污染时，如何从含噪样本协方差矩阵恢复扩散过程积分协波动率矩阵的谱分布？
- 方法与思路
- 作者建立信号与信号加噪声样本矩阵的极限谱联系，结合修正预平均构造两步估计，并另提基于标准 Marčenko–Pastur 方程的方法。
- 材料陈述的贡献
- 摘要称，两步方法可对一类扩散过程一致估计积分协波动率谱分布；另一方法更稳健并消除噪声影响，且在同步与异步情形中进行模拟。
- 阅读关注点
- 应核对维数与采样频率的联合渐近条件、噪声和扩散过程限制，以及两种方法处理异步观测与进行谱反演的具体方式。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；稳健性与消噪结论的具体条件、模拟数值未说明，不能推广至任意噪声或采样机制。
原文摘要
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is a signal-plus-noise sample covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of signal sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to consistently estimate the spectral distribution of ICV for a class of diffusion processes. An alternative approach is further proposed, which possesses several desirable properties: it is more robust, it eliminates the effects of microstructure noise, and the asymptotic relationship that enables consistent estimation of the spectral distribution of ICV is the standard Marčenko–Pastur equation. The performance of the two approaches is examined via simulation studies under both synchronous and asynchronous observation settings.