On the estimation of integrated covariance matrices of high dimensional diffusion processes

Annals of Statistics

Volumn 39, Issue 6, 2011, Pages 3121-3151

  Zheng, Xinghua ^a   Li, Yingying ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

High dimension; High frequency; Integrated covariance matrix; Mar enko Pastur equation; Realized covariance matrix; Weighted sample covariance matrix

Indexed keywords

EID: 84862846553     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS939     Document Type: Article

References (26)

1. ADMATI, A. R. and PFLEIDERER, P. (1988). A theory of intraday patterns: Volume and price variability. Rev. Financ. Stud. 1 3-40.
2. ANDERSEN, T. G. and BOLLERSLEV, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance 4 115-158.
3. ANDERSEN, T. G. and BOLLERSLEV, T. (1998). Deutsche mark-dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies. J. Finance 53 219-265.
4. ANDERSEN, T. G., BOLLERSLEV, T., DIEBOLD, F. X. and LABYS, P. (2001). The distribution of realized exchange rate volatility. J. Amer. Statist. Assoc. 96 42-55. MR1952727
5. BAI, Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9 611-677. MR1711663
6. BAI, Z., CHEN, J. and YAO, J. (2010). On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Aust. N. Z. J. Stat. 52 423-437. MR2791528
7. BAI, Z., LIU, H. and WONG, W.-K. (2009). Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Math. Finance 19 639-667. MR2583523
8. BAI, Z. D. and SILVERSTEIN, J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab. 26 316-345. MR1617051
9. BARNDORFF-NIELSEN, O. E. and SHEPHARD, N. (2004). Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica 72 885-925. MR2051439
10. BARNDORFF-NIELSEN, O. E., HANSEN, P. R., LUNDE, A. and SHEPHARD, N. (2011). Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. J. Econometrics 162 149-169.
11. EL KAROUI, N. (2008). Spectrum estimation for large dimensional covariance matrices using random matrix theory. Ann. Statist. 36 2757-2790. MR2485012
12. FAN, J., LI, Y. and YU, K. (2011). Vast volatility matrix estimation using high frequency data for portfolio selection. J. Amer. Statist. Assoc. To appear.
13. GERONIMO, J. S. and HILL, T. P. (2003). Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform. J. Approx. Theory 121 54-60. MR1962995
14. HORN, R. A. and JOHNSON, C. R. (1990). Matrix Analysis. Cambridge Univ. Press, Cambridge. Corrected reprint of the 1985 original. MR1084815
15. JACOD, J. and PROTTER, P. (1998). Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 267-307. MR1617049
16. MARCENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 507-536. MR0208649
17. MARKOWITZ, H. (1952). Portfolio selection. J. Finance 7 77-91.
18. MARKOWITZ, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. Cowles Foundation for Research in Economics at Yale University, Monograph 16. Wiley, New York. MR0103768
19. MESTRE, X. (2008). Improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates. IEEE Trans. Inform. Theory 54 5113-5129. MR2589886
20. SILVERSTEIN, J. W. (1995). Strong convergence of the empirical distribution of eigenvalues of largedimensional random matrices. J. Multivariate Anal. 55 331-339. MR1370408
21. SILVERSTEIN, J.W. and BAI, Z. D. (1995). On the empirical distribution of eigenvalues of a class of large-dimensional random matrices. J. Multivariate Anal. 54 175-192. MR1345534
22. SILVERSTEIN, J.W. and CHOI, S.-I. (1995). Analysis of the limiting spectral distribution of largedimensional random matrices. J. Multivariate Anal. 54 295-309. MR1345541
23. TAO, M.,WANG, Y., YAO, Y. and ZOU, J. (2011). Large volatility matrix inference via combining low-frequency and high-frequency approaches. J. Amer. Statist. Assoc. 106 1025-1040.
24. WANG, Y. and ZOU, J. (2010). Vast volatility matrix estimation for high-frequency financial data. Ann. Statist. 38 943-978. MR2604708
25. YIN, Y. Q. (1986). Limiting spectral distribution for a class of random matrices. J. Multivariate Anal. 20 50-68. MR0862241
26. ZHENG, X. and LI, Y. (2011). Supplement to "On the estimation of integrated covariance matrices of high dimensional diffusion processes." DOI:10.1214/11-AOS939SUPP.