ANALYSIS OF THE TIME EVOLUTION OF NON-LINEAR FINANCIAL NETWORKS

Authors

  • Paweł Fiedor Cracow University of Economics Rakowicka 27, 31-510 Kraków, Poland

DOI:

https://doi.org/10.18778/0208-6018.314.09

Keywords:

financial networks, non-linear dependence, maximum correlation coefficient, canonical-correlation analysis

Abstract

We treat financial markets as complex networks. It is commonplace to create a filtered graph (usually a Minimally Spanning Tree) based on an empirical correlation matrix. In our previous studies we have extended this standard methodology by exchanging Pearson’s correlation coefficient with information—theoretic measures of mutual information and mutual information rate, which allow for the inclusion of non-linear relationships. In this study we investigate the time evolution of financial networks, by applying a running window approach. Since information—theoretic measures are slow to converge, we base our analysis on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient, estimated by the Randomized Dependence Coefficient (RDC). It is defined in terms of canonical correlation analysis of random non-linear copula projections. On this basis we create Minimally Spanning Trees for each window moving along the studied time series, and analyse the time evolution of various network characteristics, and their market significance. We apply this procedure to a dataset describing logarithmic stock returns from Warsaw Stock Exchange for the years between 2006 and 2013, and comment on the findings, their applicability and significance.

Downloads

Download data is not yet available.

References

Abhyankar A., Copeland L., Wong, W. (1995), Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom, The Economic Journal, 105(431), 864–880.
Google Scholar

Abhyankar A., Copeland L., Wong W. (1997), Uncovering Nonlinear Structure in Real-Time Stock Market Indices, Journal of Business & Economic Statistics, 15(1), 1–14.
Google Scholar

Albert R., Barabasi L.A. (2000), Topology of evolving networks: Local Events and Universality, Physical Review Letters, 85, 5234–5237.
Google Scholar

Ammermann P.A., Patterson D.M. (2003), The cross-sectional and cross-temporal universality of nonlinear serial dependencies: Evidence from world stock indices and the Taiwan Stock Exchange, Pacific-Basin Finance Journal, 11(2), 175–195.
Google Scholar

Aste T., Shaw W., Matteo T.D. (2010), Correlation structure and dynamics in volatile markets, New Journal of Physics, 12, 085009.
Google Scholar

Bach F.R., Jordan M.I. (2002), Kernel independent component analysis, Journal of Machine Learning Research, 3, 1–48.
Google Scholar

Bonanno G., Vandewalle N., Mantegna R.N. (2000), Taxonomy of stock market indices, Physical Review E, 62(6), 7615–7618.
Google Scholar

Breiman L., Friedman J.H. (1985), Estimating Optimal Transformations for Multiple Regression and Correlation, Journal of the American Statistical Association, 80(391), 580–598.
Google Scholar

Brock W.A., Hsieh D.A., LeBaron B. (1991), Non-linear Dynamics, Chaos, and Instability. Statistical Theory and Economic Evidence, MIT Press, Cambridge.
Google Scholar

Brooks C. (1996), Testing for non-linearity in daily sterling exchange rates, Applied Financial Economics, 6(4), 307–317.
Google Scholar

Chen P. (1996), A Random Walk or Color Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes, Studies in Nonlinear Dynamics and Econometrics, 1(2), 87–103.
Google Scholar

Cover T., Thomas, J. (1991), Elements of Information Theory, John Wiley & Sons, New York.
Google Scholar

Dorogovtsev S.N., Goltsev A.V., Mendes J.F.F. (2008), Critical phenomena in complex networks, Review of Modern Physics, 80, 1275–1335.
Google Scholar

Fenn D., Porter M., Williams S., McDonald M., Johnson N., Jones N. (2011), Temporal Evolution of Financial Market Correlations, Physical Review E, 84(2), 026109.
Google Scholar

Fiedor P. (2014a), Frequency Effects on Predictability of Stock Returns. In Proceedings of the IEEE Computational Intelligence for Financial Engineering & Economics 2014, 247–254, IEEE, London.
Google Scholar

Fiedor P. (2014b), Information-theoretic approach to lead-lag effect on financial markets, European Physical Journal B, 87, 168.
Google Scholar

Fiedor P. (2014c), Networks in financial markets based on the mutual information rate, Physical Review E, 89, 05280881.
Google Scholar

Fiedor P. (2014d), Sector strength and efficiency on developed and emerging financial markets, Physica A, 413, 180–188.
Google Scholar

Gebelein H. (1941), Das statistische Problem der Korrelation als Variations- und Eigenwertproblem und sein Zusammenhang mit der Ausgleichsrechnung, Zeitschrift für Angewandte Mathematik und Mechanik, 21(6), 364–379.
Google Scholar

Gretton A., Bousquet O., Smola A., Scholkopf B. (2005), Measuring statistical dependence with Hilbert-Schmidt norms. In Proceedings of the 16th international conference on Algorithmic Learning Theory, 63–77, Springer-Verlag, Budapest.
Google Scholar

Hardle W.K., Simar L. (2007), Applied Multivariate Statistical Analysis, Springer, New York.
Google Scholar

Hardoon D., Shawe-Taylor J. (2009), Convergence analysis of kernel canonical correlation analysis: theory and practice, Machine Learning, 74(1), 23–38.
Google Scholar

Hsieh D. (1989), Testing for Nonlinear Dependence in Daily Foreign Exchange Rates, Journal of Business, 62(3), 339–368.
Google Scholar

Laloux L., Cizeau P., Potters M., Bouchaud J. (2000), Random matrix theory and financial correlations, International Journal of Theoretical & Applied Finance, 3, 391–398.
Google Scholar

Lopez-Paz D., Hennig P., Scholkopf B. (2013), The Randomized Dependence Coefficient, arXiv, stat.ML, 1304.7717.
Google Scholar

Mandelbrot B.B. (1963), The Variation of Certain Speculative Prices, Journal of Business, 36(4), 394–419.
Google Scholar

Mantegna R. (1999), Hierarchical structure in financial markets, European Physical Journal B, 11, 193–197.
Google Scholar

Mantegna R. (1991), Levy Walks and Enhanced Diffusion in Milan Stock Exchange, Physica A, 179, 232–242.
Google Scholar

McDonald M., Suleman O., Williams S., Howison S., Johnson N.F. (2005), Detecting a currency’s dominance or dependence using foreign exchange network trees, Physical Review E, 72, 046106.
Google Scholar

Nelsen R. (2006), An Introduction to Copulas. Springer Series in Statistics, Springer, New York.
Google Scholar

Paninski L. (2003), Estimation of entropy and mutual information, Neural Computation, 15, 1191–1254.
Google Scholar

Plerou V., Gopikrishnan P., Rosenow B., Nunes-Amaral L.A., Stanley H.E. (1999), Universal and Non-Universal Properties of Cross-Correlations in Financial Time Series, Physical Review Letters, 83(7), 1471–1474.
Google Scholar

Poczos B., Ghahramani Z., Schneider J. (2012), Copula-based kernel dependency measures. In Proceedings of the 29th International Conference on Machine Learning (ICML-12), 775-782, Edinburgh.
Google Scholar

Qi M. (1999), Nonlinear Predictability of Stock Returns Using Financial and Economic Variables, Journal of Business & Economic Statistics, 17(4), 419–429.
Google Scholar

Rahimi A., Recht B. (2008), Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. In Proceedings of the 2008 Conference Advances in Neural Information Processing Systems 21, 1313–1320, MIT Press, Cambridge.
Google Scholar

Rényi A. (1959), On measures of dependence, Acta Mathematica Academiae Scientiarum Hungaricae, 10, 441–451.
Google Scholar

Reshef D.N., Reshef Y.A., Finucane H.K., Grossman S.R., McVean G., Turnbaugh P.J., Lander E.S., Mitzenmacher M., Sabeti P.C. (2011), Detecting novel associations in large data sets, Science, 334(6062), 1518–1524.
Google Scholar

Sandoval L., Franca I.D.P. (2012), Correlation of financial markets in times of crisis, Physica A, 391, 187–208.
Google Scholar

Sienkiewicz A., Gubiec T., Kutner R., Struzik Z.R. (2013), Dynamic Structural and Topological Phase Transitions on the Warsaw Stock Exchange: A Phenomenological Approach, Acta Physica Polonica A, 123(3), 615–635.
Google Scholar

Sornette, D., Andersen J. (2002), A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles, International Journal of Modern Physics C, 13(2), 171–188.
Google Scholar

Szekely G.J., Rizzo M.L., Bakirov N.K. (2007), Measuring and testing dependence by correlation of distances, Annals of Statistics, 35(6), 2769–2794.
Google Scholar

Tumminello M., Aste T., Matteo T.D., Mantegna, R. (2005), A tool for filtering information in complex systems, Proceedings of the National Academy of Science USA, 102(30), 10421–10426.
Google Scholar

Tumminello M., Aste T., Matteo T.D., Mantegna R. (2007a), Correlation based networks of equity returns sampled at different time horizons, European Physical Journal B, 55(2), 209–217.
Google Scholar

Tumminello M., Coronnello C., Lillo F., Micciche S., Mantegna R. (2007b), Spanning trees and bootstrap reliability estimation in correlation-based networks, International Journal of Bifurcation & Chaos, 17, 2319–2329.
Google Scholar

Downloads

Additional Files

Published

2016-02-29

How to Cite

Fiedor, P. (2016). ANALYSIS OF THE TIME EVOLUTION OF NON-LINEAR FINANCIAL NETWORKS. Acta Universitatis Lodziensis. Folia Oeconomica, 3(314). https://doi.org/10.18778/0208-6018.314.09

Issue

Section

MSA2015

Similar Articles

<< < 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 > >> 

You may also start an advanced similarity search for this article.