Random matrix application to correlations amongst the volatility of assets

References

• Allez, R. and Bouchaud, J.-P., Eigenvector dynamics: General theory and some applications. Phys. Rev. E, 2012, 86(4), 046202.
   Web of Science ®Google Scholar
• Allez, R. and Bouchaud, J.-P., Eigenvector dynamics under free addition. Random Matrices: Theor. Appl., 2014, 3, 1450010.
   Google Scholar
• Andersen, T.G. and Bollerslev, T., Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Int. Econ. Rev., 1998, 39(4), 885–905.
   Web of Science ®Google Scholar
• Bauwens, L., Laurent, S. and Rombouts, J.V.K., Multivariate garch models: A survey. J. Appl. Econometr., 2006, 21(1), 79–109.
   Web of Science ®Google Scholar
• Black, F., Studies of stock price volatility changes. In Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, pp. 177–181, 1976 (Washington, DC).
   Google Scholar
• Bollerslev, T., Generalized autoregressive conditional heteroskedasticity. J. Econometr., 1986, 31(3), 307–327.
   Web of Science ®Google Scholar
• Borghesi, C., Marsili, M. and Miccichè, S., Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode. Phys. Rev. E, 2007, 76(2), 026104.
   Web of Science ®Google Scholar
• Bouchaud, J.P. and Potters, M., Financial applications of random matrix theory: A short review. 2009, arXiv:q-fin/0910.1205.
   Google Scholar
• Bouchaud, J.P. and Potters, M., Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, 2003 (Cambridge University Press: New York).
   Google Scholar
• Bouchaud, J.-P. and Potters, M., More stylized facts of financial markets: Leverage effect and downside correlations. Physica A, 2001, 299(1–2), 60–70.
   Web of Science ®Google Scholar
• Brody, T.A., Flores, J., French, J.B., Mello, P.A., Pandey, A. and Wong, S.S.M., Random-matrix physics: Spectrum and strength fluctuations. Rev. Mod. Phys., 1981, 53, 385–479.
   Web of Science ®Google Scholar
• Bruus, H. and Anglès d’Auriac, J.C., The spectrum of the two-dimensional Hubbard model at low filling. EPL (Europhysics Letters), 1996, 35(5), 321–326.
   Google Scholar
• Chicheportiche, R. and Bouchaud, J.-P., The joint distribution of stock returns is not elliptical. Int. J. Theor. Appl. Finance, 2012, 15(03), 1250019.
   Google Scholar
• Chicheportiche, R. and Bouchaud, J.-P., A nested factor model for non-linear dependencies in stock returns. Quant. Finance, 2015, 1–16. doi: 10.1080/14697688.2014.994668.
   Google Scholar
• Conlon, T., Ruskin, H.J. and Crane, M., Cross-correlation dynamics in financial time series. Phys. A Stat. Mech. Appl., 2009, 388, 705–714.
   Web of Science ®Google Scholar
• Coronnello, C., Tumminello, M., Lillo, F., Micciche, S. and Mantegna, R.N., Sector identification in a set of stock return time series traded at the London stock exchange. Acta Phys. Pol. B, 2005, 36, 2653–2679.
   Google Scholar
• Daly, J., Crane, M. and Ruskin, H.J., Random matrix theory filters in portfolio optimisation: A stability and risk assessment. Physica A, 2008, 387(16–17), 4248–4260.
   Web of Science ®Google Scholar
• Daly, J., Crane, M. and Ruskin, H.J., Random matrix theory filters and currency portfolio optimisation. J. Phys: Conf. Ser., 2010, 221(1), 012003.
   Google Scholar
• Engle, R.F., Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 1982, 50(4), 987–1007.
   Web of Science ®Google Scholar
• Engle, R., Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Bus. Econ. Stat., 2002, 20(3), 339–350.
   Web of Science ®Google Scholar
• Engle, R.F. and Figlewski, S., Modeling the dynamics of correlations among implied volatilities. Rev. Finance, 2014, 1–28.
   Google Scholar
• Fenn, D.J., Porter, M.A., Williams, S., McDonald, M., Johnson, N.F. and Jones, N.S., Temporal evolution of financial-market correlations. Phys. Rev. E, 2011, 84(2), 026109.
   Web of Science ®Google Scholar
• Ghalanos, A., rugarch: Univariate GARCH models. 2013. R package version 1.2–7.
   Google Scholar
• Giada, L. and Marsili, M., Data clustering and noise undressing of correlation matrices. Phys. Rev. E, 2001, 63(6), 061101.
   Web of Science ®Google Scholar
• Gopikrishnan, P., Rosenow, B., Plerou, V. and Stanley, H.E., Identifying business sectors from stock price fluctuations. 2000, arXiv:cond-mat/0011145.
   Google Scholar
• Gopikrishnan, P., Rosenow, B., Plerou, V. and Stanley, H.E., Quantifying and interpreting collective behavior in financial markets. Phys. Rev. E, 2001, 64, 035106.
   PubMed Web of Science ®Google Scholar
• Hyndman, R.J. with contributions from Athanasopoulos, G., Razbash, S., Schmidt, D., Zhou, Z., Khan, Y. and Bergmeir, C., forecast: Forecasting functions for time series and linear models, 2013. R package version 4.06.
   Google Scholar
• Guhr, T., Groeling, A.M. and Weidenmüller, H.A., Random-matrix theories in quantum physics: Common concepts. Phys. Rep., 1998, 299(4–6), 189–425.
   Google Scholar
• Hyndman, R.J. and Yeasmin K., Automatic time series forecasting: The forecast package for R. J. Stat. Softw., 2008, 27(3), 1–22.
   Web of Science ®Google Scholar
• Laloux, L., Cizeau, P., Bouchaud, J.-P. and Potters, M., Noise dressing of financial correlation matrices. Phys. Rev. Lett., 1999, 83, 1467–1470.
   Web of Science ®Google Scholar
• Liu, Y., Gopikrishnan, P., Cizeau, P., Meyer, M., Peng, C.-K. and Stanley, H.E., Statistical properties of the volatility of price fluctuations. Phys. Rev. E, 1999, 60, 1390–1400.
   PubMed Web of Science ®Google Scholar
• Lunde, A. and Hansen, P.R., A forecast comparison of volatility models: Does anything beat a garch(1,1)? J. Appl. Econometr., 2005, 20(7), 873–889.
   Web of Science ®Google Scholar
• Mantegna, R.N., Hierarchical structure in financial markets. Eur. Phys. J. B, 1999, 11(1), 193–197.
   Web of Science ®Google Scholar
• Marčenko, V.A. and Pastur, L.A., Distribution of eigenvalues for some sets of random matrices. Math. USSR-Sbornik, 1967, 1(4), 457–483.
   Google Scholar
• Markowitz, H., Portfolio selection. J. Finance, 1952, 7(1), 77–91.
   Web of Science ®Google Scholar
• Mehta, M., Random Matrices, 1995 (Academic Press: New York).
   Google Scholar
• Pafka, S., Potters, M. and Kondor I., Exponential weighting and random-matrix-theory-based filtering of financial covariance matrices for portfolio optimization. 2004, arXiv:cond-mat/0402573.
   Google Scholar
• Papp, G., Pafka, S., Nowak, M.A. and Kondor, I., Random matrix filtering in portfolio optimization. Acta Phys. Pol., B, 2005, 36, 2757–2765.
   Web of Science ®Google Scholar
• Plerou, V., Gopikrishnan, P., Rosenow, B., Nunes Amaral, L.A. and Stanley, H.E., Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett., 1999, 83, 1471–1474.
   Web of Science ®Google Scholar
• Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A., Guhr, T. and Stanley, H.E., Random matrix approach to cross correlations in financial data. Phys. Rev. E, 2002, 65(6), 066126.
   Web of Science ®Google Scholar
• Richmond, P., Urbanowicz, K. and Holyst, J.A., Risk evaluation with enhanced covariance matrix. Physica A, 2007, 384(2), 468–474.
   Web of Science ®Google Scholar
• Sengupta, A.M. and Mitra, P.P., Distributions of singular values for some random matrices. Phys. Rev. E, 1999, 60(3), 3389–3392.
   PubMed Web of Science ®Google Scholar
• Sharifi, S., Crane, M., Shamaie, A. and Ruskin, H., Random matrix theory for portfolio optimization: A stability approach. Physica A, 2004, 335(3–4), 629–643.
   Web of Science ®Google Scholar
• Tsay, R.S., Analysis of Financial Time Series (CourseSmart), 2010 (Wiley: Hoboken, NJ).
   Google Scholar
• Vandewalle, N., Bonanno, G. and Mantegna, R.N., Taxonomy of stock market indices. Phys. Rev. E, 2000, 62, 7615–7618.
   Web of Science ®Google Scholar
• Yahoo!finance. (2013). Available online at: https://ca.finance.yahoo.com/.
   Google Scholar