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

Abstract

It is increasingly important in financial economics to estimate volatilities of asset returns. However most the available methods are not directly applicable 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 overcome those difficulties we explore a novel approach that combines high-frequency volatility matrix estimation together with low-frequency dynamic models. The proposed methodology consists of three steps: (i) estimate daily realized co-volatility matrices directly based on high-frequency data, (ii) fit a matrix factor model to the estimated daily covolatility matrices, and (iii) fit a vector autoregressive (VAR) model to the estimated volatility factors. 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. Our theory shows that the relevant eigenvalues and eigenvectors can be consistently estimated. We illustrate the methodology with the high-frequency price data on several hundreds of stocks traded in Shenzhen and Shanghai Stock Exchanges over a period of 177 days in 2003. Our approach pools together the strengths of modeling and estimation at both intradaily (high-frequency) and interdaily (low-frequency) levels.

Regime-switching factor models for high-dimensional time series

“…This estimation procedure has been used for one-regime factor models with stationary processes in Tao et al (2011) andBathia (2011), and with nonstationary processes in Chang, Guo, and Yao (2013). Many numerical results show that the estimation of the loading space is not sensitive to the choice of l 0 ; see Lam, Yao, and Bathia (2011), Lam and Yao (2012), and Chang, Guo, and Yao (2013.…”

Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance

“…We can also estimate Σ ζζ byΣ ζζ =Â ΣÂ . Tao et al (2011) showed the consistency ofB andΩ t for fixed k, under several kinds of realized covariance matrices developed by Barndorff-Nielsen et al (2008, 2011), Christensen, Kinnebrock, and Podolskij (2010, Griffin and Oomen (2011), Hautsch, Kyj, and Oomen (2012), Wong and Zou (2010 and Zhang (2011). It is straightforward to show the consistency ofφ t andΣ ζζ by applying the framework of Tao et al…”

“…By using the sequence of realized covariance matrix, Tao et al (2011) developed a technique to estimate the factor covariance matrix, Ω t . We will shortly explain the approach.…”

Bayesian Parametric and Semiparametric Factor Models for Large Realized Covariance Matrices

“…The approach by Tao et al (2011) and extensions in Shen et al (2015) and Asai & McAleer (2015) decompose the RCOV matrix in a similar fashion to Engle et al (1990). Asai & McAleer (2015) model the decomposed factor in a number of ways including time-series models with long-memory, asymmetric effects and as a conditional autoregressive Wishart model.…”