Complex networks and spectral methods : an econophysics approach to equity markets

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Doctoral thesis (article-based)
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Date
2009
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en
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Verkkokirja (1852 KB, 40 s.)
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Abstract
In analysing the top-level structure of financial markets rough simplifications are often needed due to their high degree of complexity. The framework of complex networks provides a modern way to do this effectively. In this approach, a market is seen as a network, such that the nodes of the network correspond to market participants and the links reflect the dynamic interactions between them. This thesis contributes to the analysis of equity returns from the network point of view. By using empirical data on stock exchanges, we show how the general problem of extracting information from correlated time series can be formulated as a network problem. Then, we apply and develop network methods in order to analyse this problem. The purpose of the research is two folded. On the one hand, the goal is to extract new information on financial markets. On the other hand financial markets are seen as a data-rich test-bed for developing new methods and theories of more general interest. In addition to network methods, correlations between equity returns are analysed on the basis of the spectral properties of the correlation matrix. We show how these two approaches can be combined to study the top-level structure of equity markets, and believe that the results are of very general interest as well. Most emphasis is given to the analysis of the information content of correlation matrices of equity returns.
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complex networks, spectral methods, equity markets, correlation matrices
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  • [Publication 1]: Tapio Heimo, Jari Saramäki, Jukka-Pekka Onnela, and Kimmo Kaski. 2007. Spectral and network methods in the analysis of correlation matrices of stock returns. Physica A, volume 383, number 1, pages 147-151.
  • [Publication 2]: Tapio Heimo, Gergely Tibély, Jari Saramäki, Kimmo Kaski, and János Kertész. 2008. Spectral methods and cluster structure in correlation-based networks. Physica A, volume 387, number 23, pages 5930-5945.
  • [Publication 3]: Tapio Heimo, Jussi M. Kumpula, Kimmo Kaski, and Jari Saramäki. 2008. Detecting modules in dense weighted networks with the Potts method. Journal of Statistical Mechanics: Theory and Experiment, volume 2008, number 08, P08007.
  • [Publication 4]: Tapio Heimo, Kimmo Kaski, and Jari Saramäki. 2009. Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks. Physica A, volume 388, numbers 2-3, pages 145-156.
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