Large Volatility Matrix Inference via Combining Low-Frequency and High-Frequency Approaches

• Activity Number: 636
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yazhen Wang*+ and Minjing Tao and Qiwei Yao
• Companies: University of Wisconsin at Madison and University of Wisconsin at Madison and London School of Economics
• Keywords: dimension reduction ; eigen-analysis ; matrix factor model ; high-frequency data ; realized volatility matrix ; vector autoregressive model

Abstract

It is increasingly popular in financial economics to estimate volatilities of asset returns. However most the available methods are not directly relevant when the number of assets involved is large, due to the lack of accuracy in estimating high dimensional matrices. Therefore it is pertinent to reduce the effective size of volatility matrices in order to produce adequate estimates and forecasts. Furthermore, since high-frequency financial data for different assets are typically not recorded at the same time points, conventional dimension-reduction techniques are not directly applicable. To tackle the challenges this paper explores a novel approach that combines high-frequency volatility matrix estimation together with low-frequency dynamic models. We establish the asymptotic theory for the proposed methodology in the framework that allows sample size, number of assets, and number of days go to infinity together. We illustrate the methodology with the high-frequency price data. Our approach pools together the strengths of modeling and estimation at both intradaily (high-frequency) and interdaily (low-frequency) levels.