Random matrix ensembles of time-lagged correlation matrices: Derivation of eigenvalue spectra and analysis of financial time-series

Quantitative Finance

Volumn 8, Issue 7, 2008, Pages 705-722

  Biely, Christoly ^a,b   Thurner, Stefan ^a,b  

^a MEDICAL UNIVERSITY OF VIENNA   (Austria)

^b SANTA FE INSTITUTE   (United States)

Author keywords

Adaptive behaviour; Agent based modelling; Asset pricing; Complexity in economics; Financial time series; Stochastic analysis

Indexed keywords

EID: 54349101607     PISSN: 14697688     EISSN: 14697696     Source Type: Journal    
DOI: 10.1080/14697680701691477     Document Type: Article

References (41)

1. Asaki, T.J., Chartrand, R., Vixie, K.R. and Wohlberg, B., Abel inversion using total-variation regularization. Inverse Prob., 2005, 21, 1895-1903.
2. Badrinath, S.G., Kale, J.R. and Noe, T.H., Of shepherds, sheep, and the cross-autocorrelations in equity returns. Rev. Finan. Stud., 1995, 8, 401-430.
3. Bernhardt, D. and Davies, R.J., Portfolio cross-autocorrelation puzzles. 2005 (Working Paper).
4. Bouchaud, J.P., Private communication, 2006.
5. Bouchaud, J.P., Laloux, L., Augusta, M.M. and Potters, M., Large dimension forecasting models and random singular value spectra. Eur. Phys. J. B, 2007, 55, 201-207.
6. Bouchaud, J.P. and Potters, M., Theory of Financial Risk, 2000 (Cambridge University Press: Cambridge).
7. Boudoukh, J., Richardson, R. and Whitelaw, R., A tale of three schools: insights on autocorrelation of short-horizon returns. Rev. Finan. Stud., 1994, 7, 539-573.
8. Bracewell, R., The Fourier Transform and its Applications, 1965 (McGraw-Hill: New York).
9. Brennan, M.J., Jegadeesh, N. and Swaminathan, B., Investment analysis and the adjustment of stock prices to common information. Rev. Finan. Stud., 1993, 6, 799-824.
10. Burda, Z., Janik, R.A., Jurkiewicz, J., Nowak, M.A., Papp, G. and Zahed, I., Free random Levy matrices. Phys. Rev. E, 2002, 65, 021106.
11. Burda, Z., Jarosz, A., Jurkiewicz, J., Nowak, M.A., Papp, G. and Zahed, I., Applying free random variables to random matrix analysis of financial data. Physics/0603024, 2006.
12. Chan, K., Imperfect information and cross-autocorrelation among stock prices. J. Finan., 1993, 48, 1211-1230.
13. Chordia, T. and Swaminathan, B., Trading volume and cross- autocorrelations in stock returns. J. Finan., 2000, 55, 913-936.
14. Cizeau, P. and Bouchaud, J.P., Theory of Levy matrices. Phys. Rev. E, 1994, 50, 1810.
15. Edelman, A., The probability that a random real Gaussian matrix has k real eigenvalues. J. Multivar. Anal., 1997, 60, 203-232.
16. Epps, T.W., Comovements in stock prices in the very short run. J. Am. Statist. Assoc., 1979, 74, 291-298.
17. Feinberg, J., Scalettar, R. and Zee, A., 'Single ring theorem' and the disk-annulus phase transition. J. Math. Phys., 2001, 42, 5718.
18. Forrester, P.J., Log-gases and random matrices. Manuscript in preparation, 2008. Available online at: www.ms.unimelb.edu.au/ matpjf/matpjf.html
19. Ginibre, J., Statistical ensembles of complex, quaternion, and real matrices. J. Math. Phys., 1965, 6, 440.
20. Girko, V.L., Spectral Theory of Random Matrices, 1988 (Russian: Nauka: Moscow).
21. Hameed, A., Time-varying factors and cross-autocorrelations in short-horizon stock returns. J. Finan. Res., 1997, 20, 435-458.
22. Kanzieper, E. and Akemann, G., Statistics of real eigenvalues in Ginibre's ensemble of random real matrices. Phys. Rev. Lett., 2005, 95, 230201.
23. Kim, D.-H. and Jeong, H., Systematic analysis of group identification in stock markets. Phys. Rev. E, 2005, 72, 046133.
24. Kullmann, L., Kertesz, J. and Kaski, K., Time dependent cross correlations between different stock returns: a directed network of influence. Phys. Rev. E, 2006, 66, 026125.
25. Laloux, L., Cizeau, P., Bouchaud, J.-P. and Potters, M., Noise dressing of financial correlation matrices. Phys. Rev. Lett., 1999, 83, 1467.
26. Lehmann, N. and Sommers, H.-J., Eigenvalue statistics of random real matrices. Phys. Rev. Lett., 1991, 67, 941.
27. Lo, A.W. and MacKinlay, A.C., When are contrarian profits due to stock market over-reaction? Rev. Finan. Stud., 1990, 3, 175-206.
28. Mantegna, R.N., Hierarchical structure in financial markets. Eur. Phys. J. B, 1999, 11, 193-197.
29. Markowitz, H.M., Portfolio selection. J. Finan., 1952, 7, 77-91.
30. Mayya, K.B.K., and Amritkar, R.E., Delay correlation matrices. cond-mat/0601279, 2006.
31. Mench, R., Portfolio return autocorrelation. J. Finan. Econ., 1993, 34, 307-344.
32. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T. and Stanley, H.E., Random matrix approach to cross correlations in financial data. Phys. Rev. E, 2002, 65, 066126.
33. Plerou, V., Goprikrishnan, P., Rosenow, B., Amaral, L.A.N. and Stanley, H.E., Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett., 1999, 83, 1471.
34. Potters, M., Bouchaud, J.P. and Laloux, L., Financial applications of random matrix theory: old laces and new pieces. Acta Phys. Pol. B, 2005, 36, 9.
35. Sharpe, W.F., Capital asset prices: a theory of market equilibrium under conditions of risk. J. Finan., 1964, 19, 425-442.
36. Sommers, H.J., Crisanti, A., Somopolinsky, H. and Stein, Y., Spectrum of large random asymmetric matrices. Phys. Rev. Lett., 1988, 60, 1895.
37. Toth, B. and Kertesz, J., Increasing market efficiency: evolution of cross-correlations of stock returns. Physica A, 2006, 360, 505.
38. Utsugi, A., Ino, K. and Oshikawa, M., Random matrix theory analysis of cross correlations in financial markets. Phys. Rev. E, 2004, 70, 026110.
39. Wigner, E.P., Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math., 1955, 62, 548.
40. Wigner, E.P., On the distribution of the roots of certain symmetric matrices. Ann. Math., 1958, 67, 325.
41. Wishart, J., The generalized product moment distribution in samples from a normal multivariate population. Biometrika, 1928, 20, 32.