High-dimensional volatility matrix estimation with high-frequency financial data: The GARCH-Itô grouped factor model

Abstract

In the research area of the high-frequency financial data analysis, estimation and prediction of the high-dimensional volatility matrix are challenging problems, especially when the assets of interest have a naturally given group structure. In order to address this issue, we propose a novel GARCH-Itôgrouped factor model, in which we present the log price series of grouped assets with common factors, group-specific factors, and an asset-specific error term. We then embed the discrete GARCH structure into the volatility of the eigenvalue processes to capture the volatility dynamics of the observed price data. We propose a quasi maximum likelihood method for parameter estimation, establish its asymptotic properties and illustrate its good finite-sample performance with simulation. In real data analysis, we compare our method with the ungrouped factor model and the nonparametric high-frequency volatility estimator MSRV using the data from the SSE Main Board and the SZSE ChiNext market, where the proposed method outperforms its competitors in terms of prediction of the volatility matrix.