
Quantitative Finance and Economics, 2018, 2(2): 413467. doi: 10.3934/QFE.2018.2.413.
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Applications of randommatrix theory and nonparametric changepoint analysis to three notable systemic crises
^{1} Canada Pension Plan Investment BoardOne Queen Street East, Suite 2500, Toronto, ON M5C 2W5, Canada
^{2} Department of Statistics & Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
^{3} School of Accounting & Finance, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Received: , Accepted: , Published:
Special Issues: Systemic Risk Measurement
Keywords: global financial crisis; Eurozone sovereign debt crisis; Asian financial crisis; equities; bonds; CDS; contract; principal component analysis; random matrix theory; nonparametric changepoint analysis
Citation: David Melkuev, Danqiao Guo, Tony S. Wirjanto. Applications of randommatrix theory and nonparametric changepoint analysis to three notable systemic crises. Quantitative Finance and Economics, 2018, 2(2): 413467. doi: 10.3934/QFE.2018.2.413
References:
 1. lez R, Bouchaud JP (2011) Individual and collective stock dynamics: intraday seasonalities. New J Phys 13: 345–349.
 2. Anderson TW (1963) Asymptotic theory for principal component analysis. Ann Math Stat 34: 122– 148.
 3. Andersson E, Bock D, Fris´en M (2004) Detection of turning points in business cycles. J Bus Cycle Manage Anal 1: 93–108.
 4. Andersson E, Bock D, Fris´en M (2006) Some statistical aspects of methods for detection of turning points in business cycles. J Appl Stat 33: 257–278.
 5. Andrews DWK, Lee I, Ploberger W (1996) Optimal changepoint tests for normal linear regression. J Econometrics 70: 9–38.
 6. Ang A, Chen J (2002) Asymmetric correlations of equity portfolios. J Financ Econ 63: 443–494.
 7. Bai Z, Zhou W (2008) Large sample covariance matrices without independence structures in columns. Stat Sinica 18: 425–442.
 8. Bai ZD, Silverstein JW (2010) Spectral Analysis of Large Dimensional Random Matrices, Second Edition, Springer, New York.
 9. Basserville M, Nikiforov I (1993) Detection of Abrupt Changes: Theory and Applications. Prentice Hall, Englewood Cli_s, NJ.
 10. Beibel M, Lerche HR (2000) A new look at optimal stopping problems related to mathematical finance. Stat Sinica 7: 93–108.
 11. Bejan A (2005) Largest eigenvalues and sample covariance matrices. M.Sc. dissertation, Department of Statistics, The University of Warwick.
 12. Berkes I, Gombay E, Horv´ath L, et al. (2004) Sequential changepoint detection in GARCH(p,q) models. Economet Theor 20: 1140–1167.
 13. Biely C, Thurner S (2008) Random matrix ensembles of timelagged correlation matrices: derivation of eigenvalue spectra and analysis of financial timeseries. Quant Financ 8: 705–722.
 14. Bijlsma M, Klomp J, Duineveld S (2010) Systemic risk in the financial sector: A review and synthesis. CPB Netherland Bureau of Economic Policy Analysis Paper 210.
 15. Billio M, Getmansky M, Lo AW, et al. (2012) Econometric measures of connectedness and systemic risk in the finance and insurance sectors. J Financ Economet 104: 535–559.
 16. Bouchaud JP, Potters M (2001) More stylized facts of financial markets: leverage effect and downside correlations. Physica A 299: 60–70.
 17. Broemling LD, Tsurumi H (1987) Econometrics and Structural Change, Marcel Dekker, New York.
 18. Capuano C (2008) The optioniPoD. The probability of default implied by option prices based on entropy. IMF.
 19. Chen J, Gupta AK (1997) Testing and locating variance changepoints with application to stock prices. J Am Stat Assoc 92: 739–747.
 20. Chordia T, Swaminathan B (2000) Trading volume and crossautocorrelations in stock returns. J Financ 55: 913–935.
 21. Cizeau P, Potters M, Bouchaud JP (2001) Correlation structure of extreme stock returns. Quant Financ 1: 217–222.
 22. Conlon T, Ruskin HJ, Crane M (2009) Crosscorrelations dynamics in financial time series. Physica A 388: 705–714.
 23. Constantine AG (1963) Some noncentral distribution problems in multivariate analysis. Ann Math Stat 34: 1270–1285.
 24. Daniel K, Moskowitz T (2016) Momentum crashes. J Financ Econ 122: 221–247.
 25. Davis RA, Pfa_el O, Stelzer R (2014) Limit theory for the largest eigenvalue of sample covariance matrices with heavytails. Stoch Proc Appl 124: 18–50.
 26. De Brandt O, Hartmann P (2000) Systemic risk: A survey. European Central Bank.
 27. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431.
 28. Dimson E (1979) Risk measurement when shares are subject to infrequent trading. J Financ Econ 7: 197–226.
 29. Doris D (2014) Modeling Systemic Risk in the Options Market. Ph.D. Thesis, Department of Mathematics, New York University, New York, NY.
 30.Drożdż S, Grumer F, Ruf F, et al. (2000) Dynamics of competition between collectivity and noise in the stock market. Physica A 287: 440–449.
 31. Edelman A, Persson PO (2005) Numerical methods for eigenvalue distributions of random matrices. Math .
 32. Edelman A, Rao NR (2005) Random matrix theory. Acta Numer 14: 233–297.
 33. Franses PH, van Dijk D (2000) NonLinear Time Series Models in Empirical Finance. Cambridge University Press, New York, NY.
 34. Geman S (1980) A limit theorem for the norm of random matrices. Ann Probab 8: 252–261.
 35. Gopikrishnan P, Rosenov B, Plerou V, et al. (2001) Quantifying and interpreting collective behavior in fnancial markets. Physi Rev E 64: 035106.
 36. Granger CWJ (1969) Investigating causal relations by econometric models and crossspectral methods. Econometrica 37: 424–438.
 37. International Monetary Fund (2009). Global Financial Stability Report; Responding to the Financial Crisis and Measuring Systemic Risks. Washington, D.C.
 38. James AT (1960) The distribution of the latent roots of the covariance matrix. Ann Math Stati 32: 874–882.
 39. Jin B, Wang C, Miao B, et al. (2009) Limiting spectral distribution of largedimensional sample covariance matrices generated by VARMA. J Multivariate Anal 100: 2112–2125.
 40. Jobst AA (2013) Multivariate dependence of implied volatilities from equity options as measure of systemic risk. International Review of Financial Analysis 28: 112–129.
 41. Johnstone IM (2001) On the distribution of the largest eigenvalue in principal component analysis. Ann Stat 29: 295–327.
 42. Kawahara Y, Yairi T, Machida K (2007) Changepoint detection in timeseries data based on subspace identification. Proceedings of the 7th IEEE International Conference on Data Mining, 559–564.
 43. Kritzman M, Li Y, Page S, et al. (2011) Principal components as a measure of systemic risk. J Portf Manage 37: 112–126.
 44. Kwiatkowski D, Phillips P, Schmidt P, et al. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series has a unit root? J Econometrics 54: 159–178.
 45. Laloux L, Cizeau P, Bouchaud JP (1999) Noise Dressing of Financial Correlation Matrices. Phys Rev Lett 83: 1467–1469.
 46. Laloux L, Cizeau P, Potters M, et al. (2000) Random matrix theory and financial correlations. Int J Theor Appl Financ 3: 391–397.
 47. Lequeux P, Menon M (2010) An eigenvalue approach to risk regimes in currency markets. J Deriv Hedge Funds 16: 123–135.
 48. Lewis M (2010) The Big Short: Inside the Doomsday Machine. W. W. Norton & Company Inc., New York, NY.
 49. Liu H, Aue A, Debashis P (2015) On the MarˇcenkoPastur law for linear time series. Ann Stat 43: 675–712.
 50. Liu S, Yamada M, Collier N, et al. (2013) Changepoint detection in timeseries data by relative densityratio estimation. Neural Networks 43: 72–83.
 51. Longin F, Solnik B (2001) Extreme correlation of international equity markets. J Financ 5: 649–676.
 52. Lorden G (1971) Procedures for reacting to a change in distribution, Ann Math Stat 42: 1897–1908.
 53.Marčenko VA, Pastur LA (1967) Distribution for some sets of random matrices. Math USSRSbornik 1: 457–483.
 54. Mayya KBK, Amritkar RE (2006) Analysis of delay correlation matrices. Quant Financ.
 55. Meng H, Xie WJ, Jiang ZQ, et al. (2014) Systemic risk and spatiotemporal dynamics of the US housing market. Sci RepUK 4: 3655.
 56. Meric I, Kim S, Kim JH, et al. (2001) Comovements of U.S., U.K., and Asian stock markets before and after September 11, 2001. J Money Invest Bank 3: 47–57.
 57. Moustakides GV (1986) Optimal stopping times for detecting changes in distributions. Ann Stat 14: 1379–1387.
 58. Muirhead RJ (1982) Aspects of Multivariate Statistical Theory, Wiley, New York.
 59. Murphy KM, Topel RH (1985) Estimation and inference in twostep econometric models. J Bus Econ Stat 34: 370–379.
 60. Newey WK,West KD (1987) A Simple, Positive Semidefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55: 703–708.
 61. NYSE Financial Index (2014) NYSE Euronex. Available from: http://www.nyse.com/about/listed/nykid.shtml.
 62. Page ES (1954) Continuous inspection schemes. Biometrika 41: 100–115.
 63. Pan RK, Sinha S (2007) Collective behavior of stock price movements in an emerging market. Phys Rev E 76: 1–9.
 64. Petterson M (1998) Monitoring a freshwater fish population: Statistical surveillance of biodiversity. Environmetrics 9: 139–150.
 65. Petzold M, Sonesson C, Bergman E, et al. (2004) Surveillance in longitudinal models: Detection of intrauterine growth restriction. Biometrics 60: 1025–1033.
 66. Phillips P, Perron P (1988) Time series regression with a unit root. Biometrika 75: 335–346.
 67. Pillai KCS (1976a) Distribution of characteristic roots in multivariate analysis. Part I: Null distributions. Can J Stat 4: 157–184.
 68. Pillai KCS (1976b) Distribution of characteristic roots in multivariate analysis. Part II: Nonnull distributions. Can J Stat 5: 1–62.
 69. Plerou V, Gopikrishnan P, Rosenow B, et al. (2002) Random matrix approach to cross correlations in financial data. Phy Rev E 65: 066126.
 70. Poor V, Hadjiliadis O (2009) Quickest Detection, Cambridge University Press, New York, NY.
 71. Preisendorfer RW (1988) Principal component analysis in meteorology and oceanography. North Holland, Amsterdam.
 72. Pukthuanthong K, Roll R (2009) Global market integration: An alternative measure and its application. J Financ Econ 94: 214–232.
 73. Pukthuanthong K, Berger D (2012) Market Fragility and International Market Crashes. J Financ Econ 105: 565–580.
 74. Reinhart C, Rogoff K (2011) This Time Is Di_erent: Eight Centuries of Financial Folly. Princeton University Press, Princeton, New Jersey.
 75. Fitch cuts Greece's issuer default ratings to 'RD'. (2012, March 9). Reuters. Available from: http://www.reuters.com/article/2012/03/09/idUSL2E8E97FN20120309.
 76. Shiryaev AN (1978) Optimal Stopping Rules. SpringerWerlag, New York.
 77. Shiryaev AN (2002) Quickest detection problems in the technical analysis of financial data. Mathematical Finance  Bachelier Congress, 2000 (Paris). Springer, Berlin, 487–521.
 78. Silverstein JW (1985) The smallest eigenvalue of large dimensional Wishart matrix. Ann Probab 13: 1364–1368.
 79. Silverstein JW (1995) Strong convergence of the empirical distribution of eigenvalues of largedimensional random matrices. J Multivariate Anal 55: 331–339.
 80. Smith R, Sidel R (2010). Banks keep failing, no end in sight. Wall Street J. Available from: http://online.wsj.com/news/articles/SB20001424052748704760704575516272337762044.
 81. Solnik B, Boucrelle C, Le Fu Y (1996) International market correlation and volatility. Financ Anal J 52: 17–34.
 82. Sugiyama M, Suzuki T, Nakajima S, et al. (2008) Direct density ratio estimation in highdimensional spaces, Ann I Stat Math 60: 699–746.
 83. Tartakovsky AG, Rozovskii BL, Blazek RB, et al. (2006) A novel approach to detection of intrusions in computer networks via adaptive sequential and batchsequential changepoint detection methods. IEEE T Signal Proces 54: 3372–3382.
 84. Thottan M, Ji C (2003) Anomaly detection in IP networks. IEEE T Signal Proces 15: 2191–2204.
 85. Thurner S, Biely C (2007) The eigenvalue spectrum of lagged correlation matrices. Acta Phys Pol B 38: 4111–4122.
 86. Tracy CA, Widom H (1996) On orthogonal and symplectic matrix ensembles. Commun Math Phys 177: 727–754.
 87. Trivedi R, Chandramouli R (2005) Secret key estimation in sequential steganography, IEEE T Signal Proces 53: 746–757. bibitemTulino2004 Tulino AM, Verd S (2004) Random Matrix Theory and Wireless Communications. Found Trend Commun Inf Theory 1: 1–182.
 88. Wetherhill GB, Brown DW (1991) Statistical Process Control. Chapman and Hall, London.
 89. White H (1980) A heteroskedasticityconsistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48: 817–838.
 90. Wigner EP (1955) Characteristic vectors of bordered matrices with infinite dimensions. Ann Math 62: 548–564.
 91. Wishart J (1928) The generalized product moment distribution in samples from a normal multivariate population. Biometrika 20: 32–52.
 92. Yamada M, Kimura A, Naya F, et al. (2013) Changepoint detection with feature selection in highdimensional timeseries data. Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence 171: 1827–1833.
 93. Yao JF (2012) A note on a MarˇcenkoPastur type theorem for time series. Stat Probab Letter 82: 20–28.
 94. Zhang M, Kolkiewicz AW,Wirjanto TS, et al. (2015) The impacts of financial crisis on sovereign credit risk analysis in Asia and Europe. Int J Financ Eng 2: 143–152.
Reader Comments
© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *