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Application of a New Quantitative Approach to Stock Markets: Minimum Spanning Tree

Year 2017, Volume 5, Issue 1, 2017, 163 - 169, 30.06.2017
https://doi.org/10.17093/alphanumeric.323988

Abstract

The systems involving interacting agents such as food networks, scientific citations, social networks, communication networks, the Internet, and the companies interacting in stock portfolios have long been studied by many researchers under the concept of complex systems. Such systems are expressed in terms of weighted networks. The dense connections and entwined relations amongst the agents play important roles for forecasting or risk analysis. In this study we present a novel approach to determine hierarchical structure of Industrial sector in the globally operating stock market network. By using the subdominant ultra-metric topology emerge from the minimum spanning tree of the stock market network; it becomes possible to extract the important properties of this complex system. Moreover, we use the dynamic time warping distance to determine the taxonomy and to measure similarity between time series of the operating Industrial sectors. It is found that United States, United Kingdom, Netherlands and Denmark are the most dominant stock exchanges in Industrials sector. We also find three hierarchical clusters and then topologically analyze the structure of considered clusters.

References

  • [1] Mantegna, R.N. “Hierarchical structure in financial markets” Eur. Phys. J. B (1999) 11(1) pp: 193-197. doi:10.1007/s100510050929 [2] G. Bonanno, G. Caldarelli, F. Lillo, R.N. Mantegna “Topology of correlation-based minimal spanning trees in real and model markets”, Phys. Rev. E, 68 (4) (2003), p. 046130 doi:10.1103/PhysRevE.68.046130 [3] Micciche, S., Bonanno, G., Lillo, F., Mantegna, R. N. “Degree stability of a minimum spanning tree of price return and volatility”. Physica A. 2003, vol.324, pp.66–73. doi: 10.1016/S0378-4371(03)00002-5 [4] J.-P. Onnela, A. Chakraborti, K. Kaski, J. Kertész,, and A. Kanto, “Asset Trees and Asset Graphs in Financial Markets”, Physica Scripta. (2003) Vol. T106, pp. 48–54. doi: 10.1238/Physica.Topical.106a00048 [5] J.-P. Onnela, A. Chakraborti, K. Kaski, and J. Kertész,, “Dynamic asset trees and portfolio analysis“ Eur. Phys. J. B (2002) Vol. 30, pp. 285-288. doi: 10.1140/epjb/e2002-00380-9 [6] Rešovský, M., Horváth, D., Gazda, V., & Siničáková, M., “Minimum Spanning Tree Application in the Currency” Market. Biatec, 21(7) (2013), 21-23. [7] Wang, G.J., Xie, C., Han, F., Sun, B., Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree, Physica A: Statistical Mechanics and its Applications, Vol. 391 (2012), pp. 4136-4146. [8] Hatipoglu V.F., “Sectorial Hierarchy in Borsa İstanbul”, 2nd International Annual Meeting of Sosyoekonomi Society, October 28-29, 2016, Amsterdam [9] D.J. Berndt, J. Clifford, Using dynamic time warping to find patterns in time series, Workshop on Knowledge Discovery in Database, 1994, pp. 359–370. [10] W. Jang, J. Lee, W. Chang, Currency crises and the evolution of foreign exchange market: evidence from minimum spanning tree, Physica A 390 (2011), pp.707–718. [11] J. Kwapień, S. Gworek, S. Drożdż, Structure and evolution of the foreign exchange networks, Acta Physica Polonica B 40 (2009), pp.175–194.

Yeni Bir Nicel Yaklaşımının Hisse Senedi Piyasalarına Uygulanması: Minimum Geren Ağaç

Year 2017, Volume 5, Issue 1, 2017, 163 - 169, 30.06.2017
https://doi.org/10.17093/alphanumeric.323988

Abstract

Gıda ağları, bilimsel atıflar, sosyal ağlar, iletişim ağları, internet ve etkileşen hisse senedi portföyleri gibi birbiriyle etkileşen bileşenleri içeren sistemler, karmaşık sistemler kavramı altında pek çok araştırmacı tarafından çalışılmıştır. Bu tür sistemler ağırlıklı ağlar ile ifade edilir. Yoğun ağlar ve dolaşık ilişkiler, bileşenler üzerine tahmin yapma veya risk analizi için önemli role sahiptir. Bu çalışmada sanayi sektörü hisseleri üzerinden küresel borsaların hiyerarşik yapısını elde etmek için yeni bir metot sunuyoruz. Borsa ağını minimum geren ağaçtan çıkarılan alt baskın ultrametrik topolojiyi kullanarak, karmaşık sistemlerin önemli özelliklerini çıkarmak mümkündür. Ek olarak sınıflandırma yapmak ve ele alınan sanayi sektörlerine ait zaman serileri arasındaki benzerliği ölçebilmek için dinamik zaman bükmesi uzaklığını kullandık. Sonuçta Amerika Birleşik Devletleri, İngiltere, Hollanda ve Danimarka borsalarının sanayi sektörü hisse senetleri açısından incelenenler arasında en baskın borsalar oldukları bulunmuştur. Ayrıca hiyerarşik üç küme bulduk ve bu kümelerin yapısını topolojik olarak inceledik.

References

  • [1] Mantegna, R.N. “Hierarchical structure in financial markets” Eur. Phys. J. B (1999) 11(1) pp: 193-197. doi:10.1007/s100510050929 [2] G. Bonanno, G. Caldarelli, F. Lillo, R.N. Mantegna “Topology of correlation-based minimal spanning trees in real and model markets”, Phys. Rev. E, 68 (4) (2003), p. 046130 doi:10.1103/PhysRevE.68.046130 [3] Micciche, S., Bonanno, G., Lillo, F., Mantegna, R. N. “Degree stability of a minimum spanning tree of price return and volatility”. Physica A. 2003, vol.324, pp.66–73. doi: 10.1016/S0378-4371(03)00002-5 [4] J.-P. Onnela, A. Chakraborti, K. Kaski, J. Kertész,, and A. Kanto, “Asset Trees and Asset Graphs in Financial Markets”, Physica Scripta. (2003) Vol. T106, pp. 48–54. doi: 10.1238/Physica.Topical.106a00048 [5] J.-P. Onnela, A. Chakraborti, K. Kaski, and J. Kertész,, “Dynamic asset trees and portfolio analysis“ Eur. Phys. J. B (2002) Vol. 30, pp. 285-288. doi: 10.1140/epjb/e2002-00380-9 [6] Rešovský, M., Horváth, D., Gazda, V., & Siničáková, M., “Minimum Spanning Tree Application in the Currency” Market. Biatec, 21(7) (2013), 21-23. [7] Wang, G.J., Xie, C., Han, F., Sun, B., Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree, Physica A: Statistical Mechanics and its Applications, Vol. 391 (2012), pp. 4136-4146. [8] Hatipoglu V.F., “Sectorial Hierarchy in Borsa İstanbul”, 2nd International Annual Meeting of Sosyoekonomi Society, October 28-29, 2016, Amsterdam [9] D.J. Berndt, J. Clifford, Using dynamic time warping to find patterns in time series, Workshop on Knowledge Discovery in Database, 1994, pp. 359–370. [10] W. Jang, J. Lee, W. Chang, Currency crises and the evolution of foreign exchange market: evidence from minimum spanning tree, Physica A 390 (2011), pp.707–718. [11] J. Kwapień, S. Gworek, S. Drożdż, Structure and evolution of the foreign exchange networks, Acta Physica Polonica B 40 (2009), pp.175–194.
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Details

Journal Section Articles
Authors

Veysel Fuat Hatipoğlu

Publication Date June 30, 2017
Submission Date June 29, 2017
Published in Issue Year 2017 Volume 5, Issue 1, 2017

Cite

APA Hatipoğlu, V. F. (2017). Application of a New Quantitative Approach to Stock Markets: Minimum Spanning Tree. Alphanumeric Journal, 5(1), 163-169. https://doi.org/10.17093/alphanumeric.323988

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