High-dimensional integrated volatility matrix estimation forhigh-frequency financial data with jumps

Abstract

The joint volatility matrix of assets is an important statistic for resource allocation and risk management. Accurate estimation of the joint volatility matrix is one of the hot issues in financial statistics and risk measurement. In this paper, we study theintegral volatility matrix estimation of logarithmic price data with jumps under microstructure noise including market information. When the prices are not synchronized, and the number of assets and sample size tend to infinity, four estimation methods of high-dimensional integral volatility matrices are proposed by using the non-overlapping interval method and sparse characteristics. The convergence rate can reach the optimal convergence rate of the existing high-dimensional integral volatility matrix estimation. At the same time, the proposed adjusted estimators are consistent and semi-positive definite. The advantages and disadvantages of these estimators are compared in the simulation study. Finally the proposed methods are applied to the empirical study of Shanghai Securities Index data.