Estimating high dimensional covariance matrices and its applications

Annals of Economics and Finance

Volumn 12, Issue 2, 2011, Pages 199-215

  Bai, Jushan ^a,b   Shi, Shuzhong ^c  

^a Columbia University ^*  (United States)

^b CENTRAL UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^c Peking University   (China)

Author keywords

APT; CAPM; Empirical Bayes; Factor analysis; GMM; Optimal portfolios; Principal components; Random matrix theory; Shrinkage method; Singular value decomposition

Indexed keywords

EID: 80052702459     PISSN: 15297373     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (61)

1. Anderson, T. W., 1984. An Introduction to Multivariate Statistical Analysis, John Wily & Sons.
2. Bai, J., 2003. Inferential Theory for Factor Models of Large Dimensions. Econometrica 71:1, 135-172.
3. Bai, J., 2004. Estimating Cross-Section Common Stochastic Trends in Non-Stationary Panel Data. Journal of Econometrics 122, 137-183.
4. Bai, J., 2010. Principal components and factor analysis, evaluating commonly used estimation procedures, unpublished manuscript, Department of Economics, Columbia University.
5. Bai, J. and K. P. Li, 2010. Statistical analysis of factor models of high dimension. Unpublished manuscript, Department of Economics, Columbia University.
6. Bai, J. and S. Ng, 2002. Determining the Number of Factors in Approximate Factor Models. Econometrica 70:1, 191-221.
7. Bai, J. and S. Ng, 2008. Large Dimensional Factor Models. NOW Publishing Inc.
8. Bai, J. and S. Ng, 2010. Instrumental variable estimation in a data rich environment. Econometric Theory 26, 1577-1606.
9. Bai, J. and S. Ng, 2011. Principal components estimation and identification of factors. Unpublished manuscript, Department of Economics, Columbia University.
10. Bai, Z., 1999. Methodologies in spectral analysis of large dimensional random matrices, a review. Statistica Sinica 9, 611-677.
11. Barnard, J., R. McCulloch, and X. L. Meng, 2000. Modeling Covariance Matrices In Terms Of Standard Deviations And Correlations, With Application To Shrinkage. Statistica Sinica 10, 1281-1311.
12. Bengtsson, C. and J. Holst, 2003. On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish Asset Returns. Unpublished manuscript, Department of Economics, Luud University.
13. Bollerslev, T., 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. Review of Economics and Statistics 69, 542-54
14. Campbell, J. Y., A. Lo, and A. C. MacKinlay, 1997. The Econometrics of Financial Markets. Princeton University Press, New Jersey.
15. Chamberlain, G. and M. Rothschild,1983. Arbitrage, Factor Structure and Mean-Variance Analysis in Large Asset Markets. Econometrica 51, 1305-1324.
16. Chen, C. F., 1979. Bayesian inference for a normal dispersion matrix and its application to stochastic multiple regression analysis. Journal of the Royal Statistical Society, Series B 41, 235-248.
17. Chen, N., R. Roll, and S. Ross, 1986. Economic Forces and the Stock Market. Journal of Business 59, 383-403.
18. Chib, S., F. Nardari, and N. Shephard, 2002. Analysis of High Dimensional Multivariate Stochastic Volatility Models, Working paper, Washington University in Saint Louis.
19. Connor, G. and R. A. Korajczyk, 1986. Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis. Journal of Financial Economics 15, 373C394.
20. Connor, G. and R. A. Korajczyk, 1988. Risk and Return in an Equilibrium APT: Application of a New Test Methodology. Journal of Financial Economics 21, 255C289.
21. Daniels, M. J. and R. E. Kass, 1999. Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. Journal of the American Statistical Association 94, 1254-1263.
22. Daniels, M. J. and R. E. Kass, 2001. Shrinkage Estimators for Covariance Matrices. Biometrics 57, 1173-1184.
23. Engle, R. F., 2002. Dynamic conditional correlation a simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20, 339-350.
24. Engle, R. F. and K. F. Kroner, 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122-150.
25. Engle, R. F., V. K. Ng, and M. Rothschild, 1990. Asset pricing with a factor ARCH covariance structure: empirical estimates for treasury bills. Journal of Econometrics 45, 213-238.
26. Engle, R. F. and K. Sheppard, 2001. Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, unpublished paper: UCSD.
27. Fama, E. F. and K. R. French, 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics 33, 3C56.
28. Fan, J., Y. Fan, and J. Lv, 2008. High dimensional covariance matrix estimation using a factor model. Journal of Econometrics 147, 186-187.
29. Forni, M., M. Hallin, M. Lippi, and L. Reichlin, 2000. The generalized dynamic-factor model: identification and estimation. The Review of Economics and Statistics 82, pp 540-554.
30. Gao P. J. and X. D. Huang, 2008. Aggregate Consumption-Wealth Ratio and the Cross-Section of Stock Returns: Some International Evidence. Annals of Economics and Finance 9, 1-37.
31. Gelman, A. J. B. Clarin, H. S. Stern, and D. B. Rubin, 1997. Bayesian Data Analysis, London: Chapman and Hall.
32. Han, Y., 2003. Asset Allocation with a High Dimensional Latent Factor Model. Olin School of Business Washington University in St. Louis.
33. Harvey, C. R., B. Solnik, and G. Zhou, 2002. What Determines Expected International Asset Returns? Annals of Economics and Finance 3, 249-298.
34. Jagannathan, R. and T. Ma, 2002. Risk Reduction in Large Portfolios: Why imposing the wrong constraints helps, Working Paper.
35. Jones, C. S., 2001. Extracting Factors from Heteroskedastic Asset Returns. Journal of Financial Economics 62, 293-325.
36. Kapetanios, G., 2004. A new method for determining the number of factors in factor models with large datasets. Department of Economics, Queen Mary University of London, working paper 525.
37. Laloux, L., P. Cizeau, J. P. Bouchaud, and M. Potters, 1999. Noise Dressing of Financial Correlation Matrices. Phys. Rev. Lett 83, 1467.
38. Laloux, L., P. Cizeau, J. P. Bouchaud, and M. Potters, 2000. Random matrix theory and financial correlations. International Journal of Theoretical and Applied Finance 3, 391-397.
39. Lawley D. N. and A. E. Maxwell, 1971, Factor Analysis as a Statistical Method, New York: American Elsevier Publishing Company.
40. Ledoit, O. and M. Wolf, 2003. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance 10(5), 603-621.
41. Ledoit, O. and M. Wolf, 2004. A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis 88(2), 365-411.
42. Ledoit, O., P. Santa-Clara, and M.Wolf, 2003. Flexible multivariate GARCH modeling with an application to international stock markets. The Review of Economics and Statistics 85, 735-747.
43. Lehmann, B. and D. Modest, 1988. The empirical foundations of the arbitrage pricing theory. Journal of Financial Economics 21, 213-254.
44. Lettau, M. and S. Ludvigson, 2001, Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are Time Varying. Journal of Political Economy 109:6, 1238-1287.
45. Lintner, J, 1965. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics 47:1, 1337.
46. Markowitz, H. M., 1952,. Portfolio Selection. Journal of Finance 7(1), 77-91.
47. Meng, J. G., H. Gang, and J. Bai, 2011. OLIVE: A Simple Method For Estimating Betas When Factors Are Measured With Error. Journal of Financial Research 34(1), pages 27-60.
48. Nardari, F. and J. T. Scruggs, 2003. Analysis of Linear Factor Models with Multivariate Stochastic Volatility for Stock and Bond Returns, Department of Finance Arizona State University.
49. Onatski, A., 2005. Determining the Number of Factors from Empirical Distribution of Eigenvalues. Unpublished manuscript, Department of Economics, Columbia University.
50. Pafka, S. and I. Kondor, 2003. Noisy Covariance Matrices and Portfolio Optimization II. Physica A, 319, 487-494.
51. Plerou, V., P. Gopikrishnan, B. Rosenow, L. A. Nunes Amaral, and H. E. Stanley, 1999. Universal and Non-universal Properties of Cross Correlations in Financial Time Series. Phys. Rev. Lett. 83, 1471.
52. Plerou, V., P. Gopikrishnan, B. Rosenow, L. A. N. Amaral, and H. E. Stanley, 2000. A Random Matrix Theory Approach to Financial Cross-Correlations. Physica A 267, 374-382.
53. Ross, S. A., 1976. The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory 13, 341-360.
54. Sharifi, S., M. Crane, A. Shamaie, and H. Ruskin, 2004. Random Matrix Theory for Portfolio Optimization: A stability Approach. Physica A 335, 629-643.
55. Sharpe, W., 1963. A Simplified Model for Portfolio Analysis. Management Science 79, 277-231.
56. Sharpe, W., 1964. Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance 19(3), 425-442.
57. Stock, J. H. and M. W. Watson, 2002. Forecasting Using Principal Components from a Large Number of Predictors. Journal of the American Statistical Association 97, 1167-1179.
58. Swartz, P. 2006. Global Versus Regional Systematic Risk and International Asset Allocations in Asia. Annals of Economics and Finance 7, 77-89.
59. Tsay, R. S., 2002. Analysis of Financial Time Series, Wiley New York, 303-392.
60. Wang, P., 2008. Large Dimensional Factor Models with a Multi-Level Factor Structure: Identification, Estimation and Inference. Unpublished manuscript, New York University.
61. Yang, R. and J. O. Berger, 1994. Estimation of a covariance matrix using the reference prior. Annals of Statistics 22, 1195-1121.