Robust High-dimensional Volatility Matrix Estimation for High-Frequency Factor Model.

Area of Science:

• Quantitative Finance
• Statistical Modeling
• Econometrics

Background:

• High-frequency financial data enable volatility matrix estimation over short horizons.
• Existing methods for high-dimensional Itô processes struggle with heavy-tailed financial returns.
• Microstructural noise complicates accurate volatility estimation.

Purpose of the Study:

• To develop a robust realized volatility estimator mitigating heavy-tail influence.
• To estimate large volatility matrices using a robust input and regularization.
• To establish asymptotic theories for low-rank plus sparse volatility matrices.

Main Methods:

• Utilizing the Huber loss function with a diverging threshold for robust estimation.
• Applying Principal Orthogonal Component Thresholding (POET) for regularization.
• Analyzing high-dimensional Itô processes with microstructural noise.

Main Results:

• The proposed robust estimator exhibits sub-Gaussian concentration with finite fourth moments.
• Accurate estimation of large volatility matrices with approximate factor structures is achieved.
• Asymptotic theories for low-rank plus sparse matrices are established.

Conclusions:

• The novel robust method effectively handles heavy-tailed financial data.
• The combination of Huber loss and POET provides a powerful tool for volatility matrix estimation.
• The findings offer improved statistical methods for financial econometrics.