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Effect of changing data size on eigenvalues in the Korean and Japanese stock markets

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  • Cheoljun Eom
  • Woo-Sung Jung
  • Taisei Kaizoji
  • Seunghwan Kim

Abstract

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features.

Suggested Citation

  • Cheoljun Eom & Woo-Sung Jung & Taisei Kaizoji & Seunghwan Kim, 2008. "Effect of changing data size on eigenvalues in the Korean and Japanese stock markets," Papers 0811.4021, arXiv.org, revised Jun 2009.
    • Handle: RePEc:arx:papers:0811.4021
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    5. Eom, Cheoljun & Oh, Gabjin & Kim, Seunghwan, 2007. "Deterministic factors of stock networks based on cross-correlation in financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 139-146.
    6. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    7. Cheoljun Eom & Gabjin Oh & Seunghwan Kim, 2007. "Deterministic Factors of Stock Networks based on Cross-correlation in Financial Market," Papers 0705.0076, arXiv.org.
    8. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    9. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
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    Cited by:

    1. Eom, Cheoljun & Park, Jong Won, 2018. "A new method for better portfolio investment: A case of the Korean stock market," Pacific-Basin Finance Journal, Elsevier, vol. 49(C), pages 213-231.
    2. Eom, Cheoljun, 2017. "Two-faced property of a market factor in asset pricing and diversification effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 190-199.
    3. Bommarito, Michael J. & Duran, Ahmet, 2018. "Spectral analysis of time-dependent market-adjusted return correlation matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 273-282.
    4. Eom, Cheoljun & Park, Jong Won, 2021. "Investor attention, firm-specific characteristic, and momentum: A case of the Korean stock market," Research in International Business and Finance, Elsevier, vol. 57(C).
    5. Uechi, Lisa & Akutsu, Tatsuya & Stanley, H. Eugene & Marcus, Alan J. & Kenett, Dror Y., 2015. "Sector dominance ratio analysis of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 488-509.
    6. Eom, Cheoljun & Kaizoji, Taisei & Livan, Giacomo & Scalas, Enrico, 2021. "Limitations of portfolio diversification through fat tails of the return Distributions: Some empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    7. Eom, Cheoljun & Kwon, Okyu & Jung, Woo-Sung & Kim, Seunghwan, 2010. "The effect of a market factor on information flow between stocks using the minimal spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1643-1652.

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