Structured Volatility Matrix Estimation for Non-Synchronized High-Frequency Financial Data

Several large volatility matrix estimation procedures have been recently developed for factor-based Ito processes whose integrated volatility matrix consists of low-rank and sparse matrices. Their performance depends on the accuracy of input volatility matrix estimators. When estimating co-volatilities based on high-frequency data, one of the crucial challenges is non-synchronization for illiquid assets, which makes their co-volatility estimators inaccurate. In this paper, we study how to estimate the large integrated volatility matrix without using co-volatilities of illiquid assets. Specifically, we pretend that the co-volatilities for illiquid assets are missing, and estimate the low-rank matrix using a matrix completion scheme with a structured missing pattern. To further regularize the sparse volatility matrix, we employ the principal orthogonal complement thresholding method (POET). We also investigate the asymptotic properties of the proposed estimation procedure and demonstrate its advantages over using co-volatilities of illiquid assets. The advantages of our methods are also verified by an extensive simulation study and illustrated by high-frequency data for NYSE stocks.

[1]  M. E. Mancino,et al.  Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise , 2008, Comput. Stat. Data Anal..

[2]  Lan Zhang.  Estimating Covariation: Epps Effect, Microstructure Noise , 2006 .

[3]  Anru Zhang,et al.  Structured Matrix Completion with Applications to Genomic Data Integration , 2015, Journal of the American Statistical Association.

[4]  George Tauchen,et al.  Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance , 2012 .

[5]  Y. Z. Wang,et al.  Asymptotic nonequivalence of GARCH models and di?usions , 2002 .

[6]  Jianqing Fan,et al.  High dimensional covariance matrix estimation using a factor model , 2007, math/0701124.

[7]  D. Xiu.  Quasi-Maximum Likelihood Estimation of Volatility with High Frequency Data , 2010 .

[8]  Dacheng Xiu,et al.  Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data , 2016 .

[9]  N. Shephard,et al.  Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading , 2010 .

[10]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[11]  Nikolaus Hautsch,et al.  Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency , 2013 .

[12]  Jean Jacod,et al.  Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 , 2007 .

[13]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[14]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[15]  Harrison H. Zhou,et al.  OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS , 2013, 1309.4889.

[16]  Donggyu Kim,et al.  Asymptotic theory for large volatility matrix estimation based on high-frequency financial data , 2016 .

[17]  P. Malliavin,et al.  A Fourier transform method for nonparametric estimation of multivariate volatility , 2009, 0908.1890.

[18]  Mark Podolskij,et al.  Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data , 2010 .

[19]  Weichen Wang,et al.  An $\ell_{\infty}$ Eigenvector Perturbation Bound and Its Application , 2017, J. Mach. Learn. Res..

[20]  Jianqing Fan,et al.  Large covariance estimation by thresholding principal orthogonal complements , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[21]  Ke Yu,et al.  Journal of the American Statistical Association Vast Volatility Matrix Estimation Using High- Frequency Data for Portfolio Selection Vast Volatility Matrix Estimation Using High-frequency Data for Portfolio Selection , 2022 .

[22]  Lan Zhang.  Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach , 2004, math/0411397.

[23]  Donggyu Kim,et al.  Large volatility matrix estimation with factor-based diffusion model for high-frequency financial data , 2018, Bernoulli.

[24]  Neil Shephard,et al.  Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise , 2008 .

[25]  Maria Elvira Mancino,et al.  Fourier series method for measurement of multivariate volatilities , 2002, Finance Stochastics.

[26]  Jianqing Fan,et al.  Incorporating Global Industrial Classification Standard into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator with High Frequency Data , 2015 .

[27]  Nakahiro Yoshida,et al.  Nonsynchronous covariation process and limit theorems , 2011 .

[28]  V. Koltchinskii,et al.  Nuclear norm penalization and optimal rates for noisy low rank matrix completion , 2010, 1011.6256.

[29]  P. Mykland,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[30]  E. Fama,et al.  The Cross‐Section of Expected Stock Returns , 1992 .

[31]  Jianqing Fan,et al.  Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data , 2006 .

[32]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[33]  Jianqing Fan,et al.  Risks of Large Portfolios , 2013, Journal of econometrics.

[34]  N. Yoshida,et al.  On covariance estimation of non-synchronously observed diffusion processes , 2005 .

[35]  Seok Young Hong,et al.  Estimating the quadratic covariation matrix for asynchronously observed high frequency stock returns corrupted by additive measurement error , 2016 .

[36]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[37]  Donggyu Kim,et al.  Sparse PCA-based on high-dimensional Itô processes with measurement errors , 2016, J. Multivar. Anal..

[38]  Yazhen Wang,et al.  VAST VOLATILITY MATRIX ESTIMATION FOR HIGH-FREQUENCY FINANCIAL DATA , 2010, 1002.4754.

[39]  Jianqing Fan,et al.  High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data , 2010 .

[40]  Jianqing Fan,et al.  Robust High-Dimensional Volatility Matrix Estimation for High-Frequency Factor Model , 2017, Journal of the American Statistical Association.

[41]  Xinbing Kong.  On the systematic and idiosyncratic volatility with large panel high-frequency data , 2018, The Annals of Statistics.