Stabilization of Financial Dendrograms as a Method of Systemic Changes Measurement (A Study of TSE’s Indices)

Document Type : Original Article

Authors

1 Assistant Professor of Yazd University

2 Yazd University

Abstract

Dendrograms are considered as the most important visualization technique of Hierarchical Clustering. We studied the stability of different dendrograms on the Tehran Stock Exchange and then stabilized the system of TSE indices using Principal Component Analysis (PCA). It seems that the comparison of dendrograms before and after PCA is a quantitative measure of system stability. ( 43% in our study of 21 different indices of TSE which are the representations of the economic sectors of Iranian financial systems. We measured the similarity of different dendrograms according to Baker's Index and the Cophenetic Correlation Index. The results show that stabilized hierarchical clusterings have got better Baker's Index and more reliable dendrogram. Therefore, It is highly recommended to investors, portfolio managers and risk hedgers to denoise and stabilize their clustering with efficient methods like PCA before financial decision making.

Keywords

References

  1. Araújo, Ta., Eleuterio, S., & Louçã, F. (2018). Do sentiments influence market dynamics? A reconstruction of the Brazilian stock market and its mood. Physica A: Statistical Mechanics and its Applications, 505, 1139-1149.
  2. Baker, F. B. (1974). Stability of Two Hierarchical Grouping Techniques Case I: Sensitivity to Data Errors. Journal of the American Statistical Association, 69(346), 440-445.
  3. Bank, W. (2013). Global financial development report 2014: Financial inclusion: World Bank Publications.
  4. Brida, J. Gabriel, & Risso, W. Adrian. (2010). Hierarchical structure of the German stock market. Expert Systems with Applications, 37(5), 3846-3852.
  5. Cai, Yumei, C., Xiaomei, H., Q., & Sun, J. (2017). Hierarchy, cluster, and time-stable information structure of correlations between international financial markets. International Review of Economics & Finance, 51, 562-573
  6. Caruana, J. (2010). Systemic risk: how to deal with it? BIS Publications.
  7. de Amorim, Renato Cordeiro. (2015). Feature relevance in ward’s hierarchical clustering using the L p norm. Journal of Classification, 32(1), 46-62.
  8. Deza, Michel-Marie, & Deza, Elena. (2006). Dictionary of distances: Elsevier.
  9. Deza, Michel Marie, & Deza, Elena. (2009). Encyclopedia of distances Encyclopedia of Distances (pp. 1-583): Springer.
  10. Esmalifalak, H., Ajirlou, A. Irannezhad, B., Pordeli, S. & Esmalifalak, M. (2015). (Dis)integration levels across global stock markets: A multidimensional scaling and cluster analysis. Expert Systems with Applications, 42(22), 8393-8402.
  11. Everitt, Brian S, & Dunn, Graham. (2001). Principal components analysis. Applied multivariate data analysis, 48-73.
  12. Fang, L., Xiao, B., Yu, H., & You, Q. (2018). A stable systemic risk ranking in China’s banking sector: Based on principal component analysis. Physica A: Statistical Mechanics and its Applications, 492, 1997-2009.
  13. Fowlkes, E. B., & Mallows, C. L. (1983). A Method for Comparing Two Hierarchical Clusterings. Journal of the American Statistical Association, 78(383), 553-569.
  14. Galili, T. (2015). dendextend: an R package for visualizing, adjusting and comparing trees of hierarchical clustering. Bioinformatics, 31(22), 3718-3720.
  15. Goldberger, J., & Tassa, T. (2008). A hierarchical clustering algorithm based on the Hungarian method. Pattern Recognition Letters, 29(11), 1632-1638
  16. Guerra, S, Maria, S, Thiago C, Tabak, B Miranda P, Rodrigo A, Miranda, R (2016). Systemic risk measures. Physica A: Statistical Mechanics and its Applications, 442, 329-342.
  17. Huang, W. Q., & Wang, D. (2018). Systemic importance analysis of chinese financial institutions based on volatility spillover network. Chaos, Solitons & Fractals, 114, 19-30.
  18. Huang, W.Q., Yao, S., Zhuang, X. T., & Yuan, Y. (2017). Dynamic asset trees in the US stock market: Structure variation and market phenomena. Chaos, Solitons & Fractals, 94, 44-53.
  19. Iori, G., & Mantegna, R. N. (2018). Chapter 11 - Empirical Analyses of Networks in Finance. In C. Hommes & B. LeBaron (Eds.). Handbook of Computational Economics (Vol. 4, pp. 637-685): Elsevier.
  20. Jian, Z., Deng, P., & Zhu, Z. (2018). High-dimensional covariance forecasting based on principal component analysis of high-frequency data. Economic Modelling, 75, 422-431.
  21. Kleinow, J., Moreira, F., Strobl, S., & Vähämaa, S. (2017). Measuring systemic risk: A comparison of alternative market-based approaches. Finance Research Letters, 21, 40-46.
  22. Lahmiri, S. (2016). Clustering of Casablanca stock market based on hurst exponent estimates. Physica A: Statistical Mechanics and its Applications, 456, 310-318.
  23. Lee, Byung-Joo. (2018). Asian financial market integration and the role of Chinese financial market. International Review of Economics & Finance, 59,490-499
  24. Li, C.Z., Xu, Z.B., & Luo, T. (2013). A heuristic hierarchical clustering based on multiple similarity measurements. Pattern Recognition Letters, 34(2), 155-162.
  25. Li, We., Hommel, U., & Paterlini, S. (2018). Network topology and systemic risk: Evidence from the Euro Stoxx market. Finance Research Letters, 27,105-112
  26. Li, Y., Hao, A., Zhang, X., & Xiong, X. (2018). Network topology and systemic risk in Peer-to-Peer lending market. Physica A: Statistical Mechanics and its Applications, 508, 118-130.
  27. Lu, Ya-Nan, Li, Sai-Ping, Zhong, Li-Xin, Jiang, Xiong-Fei, & Ren, Fei. (2018). A clustering-based portfolio strategy incorporating momentum effect and market trend prediction. Chaos, Solitons & Fractals, 117, 1-15.
  28. Matsen, F. A., Billey, S. C., Kas, A., & Konvalinka, M. (2018). Tanglegrams: A Reduction Tool for Mathematical Phylogenetics. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 15(1), 343-349.
  29. Mondal, Sakib A. (2018). An improved approximation algorithm for hierarchical clustering. Pattern Recognition Letters, 104, 23-28.
  30. Nobi, A., & Lee, J. W. (2016). State and group dynamics of world stock market by principal component analysis. Physica A: Statistical Mechanics and its Applications, 450, 85-94.
  31. Rea, A., & Rea, W. (2014). Visualization of a stock market correlation matrix. Physica A: Statistical Mechanics and its Applications, 400, 109-123.
  32. Rodriguez-Moreno, M., & Peña, J. I. (2013). Systemic risk measures: The simpler the better? Journal of Banking & Finance, 37(6), 1817-1831.
  33. Sarlin, Peter, & Peltonen, Tuomas A. (2013). Mapping the state of financial stability. Journal of International Financial Markets, Institutions and Money, 26, 46-76.
  34. Scornavacca, C., Zickmann, F., & Huson, D. H. (2011). Tanglegrams for rooted phylogenetic trees and networks. Bioinformatics, 27(13), i248-i256.
  35. Sokal, R. R., & Rohlf, F. Ja. (1962). The comparison of dendrograms by objective methods. Taxon,11(2) 33-40.
  36. Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423.
  37. Tumminello, M., Lillo, F., & Mantegna, R. N. (2010). Correlation, hierarchies, and networks in financial markets. Journal of Economic Behavior & Organization, 75(1), 40-58.
  38. Venkatachalam, B., Apple, J., John, K. St., & Gusfield, D. (2010). Untangling Tanglegrams: Comparing Trees by Their Drawings. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 7(4), 588-597.
  39. Vinothkumar, K., & Selvan, M. P. (2014). Hierarchical Agglomerative Clustering Algorithm method for distributed generation planning. International Journal of Electrical Power & Energy Systems, 56, 259-269.
  40. Wang, Y., Li, H., Guan, J., & Liu, N. (2019). Similarities between stock price correlation networks and co-main product networks: Threshold scenarios. Physica A: Statistical Mechanics and its Applications, 516, 66-77.
  41. Zhao, L., Li, W., & Cai, X. (2016). Structure and dynamics of stock market in times of crisis. Physics Letters A, 380(5), 654-666.
  42. Zhao, L., Wang, G.J., Wang, M., Bao, W., Li, W., & Stanley, H. E. (2018). Stock market as temporal network. Physica A: Statistical Mechanics and its Applications, 506, 1104-1112.
Financial Management Perspective
Volume 8, Issue 24 - Serial Number 24
December 2018
Pages 103-128

Files

Share

How to cite

Statistics