Abstract
In this paper, the RMT-PCA is applied on daily-close stock prices of American Stocks in NYSE for 16 years from 1994 to 2009 to show the effectiveness and consistency of this method by analyzing the whole data of 16 years at once, as well as analyzing the cut data in various lengths between 2-8 years. The extracted trends are consistent to the actual history of the markets. The authors further analyze the intra-day stock prices of Tokyo Stock Market for 12 quarters extending from 2007 to 2009 and attempted to answer to the two remaining question of the RMT-PCA. The first issue is the number of principal components to examine, and the second issue is the number of eminent elements to examine out of the total N components of the chosen eigenvectors. While the second issue is still open, the authors have found for the first issue that only the second largest principal component is sufficient to examine, based on the comparison of this scenario and the use of the largest ten principal components. This paper argues on this point that the positive elements, and the negative elements, of the eigenvector components individually form collective modes of industrial sectors in the second eigenvector u 2, and those collective modes reveal themselves as trendy sectors of the market in that time period. The authors also discuss on the problem of setting the effective border between the noise and signals considering the artificial correlation created in the process of taking log-returns in analyzing the price time series.
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References
Mehta, M.L.: Random matrices, 3rd edn. Academic Press (2004)
Edelman, A., Rao, N.R.: Random matrix theory. Acta Numerica, 1–65 (2005)
Zhidong, B., Silverstein, J.: Spectral analysis of large dimensional Random Matrices. Springer (2010)
Tao, T., Vu, V.: Random matrices: universality of ESD and the circular law (with appendix by M. Krishnapur). Annals of Probability 38(5), 2023–2065 (2010)
Beenakker, C.W.J.: Random-matrix theory of quantum transport. Reviews of Modern Physics 69, 731–808 (1997)
Kendrick, D.: Stochastic control for economic models. McGraw-Hill (1981)
Bahcall, S.R.: Random matrix model for superconductors in a magnetic field. Physical Review Letters 77, 5276–5279 (1976)
Franchini, F., Kravtsov, V.E.: Horizon in random matrix theory, the Hawking radiation, and flow of cold atoms. Physical Review Letters 103, 166401 (2009)
Peyrache, A., et al.: Principal component analysis of ensemble recordings reveals cell assemblies at high temporal resolution. Journal of Computational Neurosience 29 (2009)
Sánchez, D., Büttiker, M.: Magnetic-field asymmetry of nonlinear mesoscopic transport. Physical Review Letters 93, 106802 (2004)
Marcenko, V.A., Pastur, L.A.: Distribution of eigenvalues for some sets of random matrices. Mathematics of the USSR-Sbornik 1, 457–483 (1994)
Sengupta, A.M., Mitra, P.P.: Distribution of singular values for some random matrices. Physical Review E 60, 3389–3392 (1999)
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Stanley, H.E.: Random matrix approach to cross correlation in financial data. Physical Review EÂ 65, 066126 (2002)
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Stanley, H.E.: Scaling behaviour in the growth of companies. Physical Review Letters 83, 1471–1474 (1999)
Laloux, L., Cizeaux, P., Bouchaud, J.-P., Potters, M.: Noise dressing of financial correlation matrix. Physical Review Letters 83, 1467–1470 (1999)
Bouchaud, J.-P., Potters, M.: Theory of Financial Risks. Cambridge Univ. Press (2000)
Mantegna, R.N., Stanley, H.E.: An Introduction to econophysics: correlations and complexity in finance. Cambridge University Press (2000)
Iyetomi, H., et al.: Fluctuation-dissipation theory of input-output interindustrial relations. Physical Review EÂ 83, 016103 (2011)
Tanaka-Yamawaki, M.: Extracting principal components from pseudo-random data by using random matrix theory. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds.) KES 2010, Part III. LNCS, vol. 6278, pp. 602–611. Springer, Heidelberg (2010)
Tanaka-Yamawaki, M.: Cross correlation of intra-day stock prices in comparison to random matrix theory. Intelligent Information Management (2011)
Yang, X., Itoi, R., Tanaka-Yamawaki, M.: Testing randomness by means of RMT formula. In: Watada, J., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds.) Intelligent Decision Technologies. SIST, vol. 10, pp. 589–596. Springer, Heidelberg (2011)
Yang, X., Tanaka-Yamawaki, M.: Testing randomness by means of Random Matrix Theory. In: 2011 Kyoto Workshop on NOLTA, p. 1 (2011)
Yang, X., Itoi, R., Tanaka-Yamawaki, M.: Testing randomness by means of Random Matrix Theory. Progress of Theoretical Physics Supplement (194), 73–83 (2012)
Tanaka-Yamawaki, M., Yang, X., Itoi, R.: Moment approach for quantitative evaluation of randomness based on RMT formula. In: Watada, J., Watanabe, T., Phillips-Wren, G., Howlett, R.J., Jain, L.C. (eds.) Intelligent Decision Technologies, Vol. 2. SIST, vol. 16, pp. 423–432. Springer, Heidelberg (2012)
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Tanaka-Yamawaki, M., Yang, X., Kido, T., Yamamoto, A. (2013). Extracting Market Trends from the Cross Correlation between Stock Time Series. In: Tweedale, J.W., Jain, L.C. (eds) Advanced Techniques for Knowledge Engineering and Innovative Applications. Communications in Computer and Information Science, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42017-7_3
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DOI: https://doi.org/10.1007/978-3-642-42017-7_3
Publisher Name: Springer, Berlin, Heidelberg
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