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Classification of international stock markets through MDS based on Hurst-surface distance

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  • Liu, Xiaoming
  • Lin, Aijing
  • Li, Shuqi

Abstract

Classifying stock markets by measuring the similarity between them can provide a reliable reference for investors and help them earn more profits. This paper seeks to explore a better method to measure the degree of similarity between international stock markets. We chose the daily closing price of 24 stock markets from the Americas, Asia, Europe, and Australia, and mapped them into three-dimensional space as points. In order to measure the similarity, we propose using Hurst-surface distance as a transformation and then use this distance matrix as a dissimilarity matrix to classify the stocks by multidimensional scaling method(MDS). We compared the classified results with classical MDS which use the Euclidean distance as a measure of similarity and σDCCA-based MDS. The results show that using Hurst-surface distance as a reflection of similarity can not only provide more information about correlation but also distinguish the differences of economic volatility in different regions. While σDCCA puts more emphasis on the similarities and dissimilarities within the same region. Those two modified MDS technology above are better than the classical method based on Euclidean, they can reflect more detailed and clearer information.

Suggested Citation

  • Liu, Xiaoming & Lin, Aijing & Li, Shuqi, 2021. "Classification of international stock markets through MDS based on Hurst-surface distance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    • Handle: RePEc:eee:phsmap:v:566:y:2021:i:c:s0378437120308839
    DOI: 10.1016/j.physa.2020.125585
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    1. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    2. Pawe{l} O'swic{e}cimka & Stanis{l}aw Dro.zd.z & Marcin Forczek & Stanis{l}aw Jadach & Jaros{l}aw Kwapie'n, 2013. "Detrended Cross-Correlation Analysis Consistently Extended to Multifractality," Papers 1308.6148, arXiv.org, revised Feb 2014.
    3. Plerou, Vasiliki & Gopikrishnan, Parameswaran & Rosenow, Bernd & Amaral, Luis A.N. & Stanley, H.Eugene, 2000. "Econophysics: financial time series from a statistical physics point of view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 443-456.
    4. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    5. Shahzad, Syed Jawad Hussain & Nor, Safwan Mohd & Mensi, Walid & Kumar, Ronald Ravinesh, 2017. "Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 351-363.
    6. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
    7. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    8. King, Mervyn A & Wadhwani, Sushil, 1990. "Transmission of Volatility between Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 5-33.
    9. M Illueca & J A Lafuente, 2002. "International stock market linkages: A factor analysis approach," Journal of Asset Management, Palgrave Macmillan, vol. 3(3), pages 253-265, December.
    10. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    11. Siqueira, Erinaldo Leite & Stošić, Tatijana & Bejan, Lucian & Stošić, Borko, 2010. "Correlations and cross-correlations in the Brazilian agrarian commodities and stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2739-2743.
    12. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    13. Zebende, G.F. & Filho, A. Machado, 2009. "Cross-correlation between time series of vehicles and passengers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4863-4866.
    14. Kenourgios, Dimitris & Samitas, Aristeidis & Paltalidis, Nikos, 2011. "Financial crises and stock market contagion in a multivariate time-varying asymmetric framework," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 21(1), pages 92-106, February.
    15. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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