Vast volatility matrix estimation for high-frequency financial data

Abstract

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In fact, they are inconsistent when both the number, $p$, of the assets and the average sample size, $n$, of the price data on the $p$ assets go to infinity. This paper proposes a new type of estimators for the integrated volatility matrix and establishes asymptotic theory for the proposed estimators in the framework that allows both $n$ and $p$ to approach to infinity. The theory shows that the proposed estimators achieve high convergence rates under a sparsity assumption on the integrated volatility matrix. The numerical studies demonstrate that the proposed estimators perform well for large $p$ and complex price and volatility models. The proposed method is applied to real high-frequency financial data.

Published in at http://dx.doi.org/10.1214/09-AOS730 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Regularized estimation of large covariance matrices
• Covariance regularization by thresholding
• Operator norm consistent estimation of large-dimensional sparse covariance matrices
• Tracy--Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices

Cited by in corpus (11)

• Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors
• On the estimation of integrated covariance matrices of high dimensional diffusion processes
• Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data
• De-biased graphical Lasso for high-frequency data
• High-dimensional estimation of quadratic variation based on penalized realized variance
• Unified Discrete-Time Factor Stochastic Volatility and Continuous-Time Ito Models for Combining Inference Based on Low-Frequency and High-Frequency
• CNN-based Realized Covariance Matrix Forecasting
• Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data
• Robust High-Dimensional Time-Varying Coefficient Estimation
• Large Volatility Matrix Prediction with High-Frequency Data
• Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance