Nonlinearity in stock networks

Chaos - Tập 28 Số 8 - 2018
David Hartman1, Jaroslav Hlinka1
1Institute of Computer Science, Czech Academy of Sciences , Prague 182 07, Czech Republic

Tóm tắt

Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna’s seminal paper, the linear Pearson’s correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possible effects of nonlinearity on the graph-theoretical properties of such networks have been demonstrated when using nonlinear measures such as mutual information instead of linear correlation. In this paper, we quantitatively characterize the nonlinearity in stock time series and the effect it has on stock network properties. This is achieved by a systematic multi-step approach that allows us to quantify the nonlinearity of coupling; correct its effects wherever it is caused by simple univariate non-Gaussianity; potentially localize in space and time any remaining strong sources of this nonlinearity; and, finally, study the effect nonlinearity has on global network properties. By applying this multi-step approach to stocks included in three prominent indices (New York Stock Exchange 100, Financial Times Stock Exchange 100, and Standard & Poor 500), we establish that the apparent nonlinearity that has been observed is largely due to univariate non-Gaussianity. Furthermore, strong nonstationarity in a few specific stocks may play a role. In particular, the sharp decrease in some stocks during the global financial crisis of 2008 gives rise to apparent nonlinear dependencies among stocks.

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Tài liệu tham khảo

2006, Complex networks: Structure and dynamics, Phys. Rep., 424, 175, 10.1016/j.physrep.2005.10.009

2009, Complex brain networks: Graph theoretical analysis of structural and functional systems, Nat. Rev. Neurosci., 10, 186, 10.1038/nrn2575

2000, The large-scale organization of metabolic networks, Nature, 407, 651, 10.1038/35036627

1977, An information flow model for conflict and fission in small groups, J. Anthropol. Res., 33, 452, 10.1086/jar.33.4.3629752

1999, Internet—Diameter of the world-wide web, Nature, 401, 130, 10.1038/43601

2003, Self-similar community structure in a network of human interactions, Phys. Rev. E, 68, 065103, 10.1103/PhysRevE.68.065103

2008, Structural insights into aberrant topological patterns of large-scale cortical networks in Alzheimer’s disease, J. Neurosci., 28, 4756, 10.1523/JNEUROSCI.0141-08.2008

2008, Disrupted small-world networks in schizophrenia, Brain, 131, 945, 10.1093/brain/awn018

2016, A climate network-based index to discriminate different types of el niño and la niña, Geophys. Res. Lett., 43, 7176, 10.1002/2016GL069119

1994, Social Network Analysis

2001, Lethality and centrality in protein networks, Nature, 411, 41, 10.1038/35075138

2000, Resilience of the internet to random breakdowns, Phys. Rev. Lett., 85, 4626, 10.1103/PhysRevLett.85.4626

2011, Analyzing and modeling real-world phenomena with complex networks: A survey of applications, Adv. Phys., 60, 329, 10.1080/00018732.2011.572452

2012, Challenges in network science: Applications to infrastructures, climate, social systems and economics, Eur. Phys. J. Spec. Top., 214, 273, 10.1140/epjst/e2012-01695-x

2003, Topology of the world trade web, Phys. Rev. E, 68, 015101, 10.1103/PhysRevE.68.015101

1999, Hierarchical structure in financial markets, Eur. Phys. J. B, 11, 193, 10.1007/s100510050929

2003, Dynamics of market correlations: Taxonomy and portfolio analysis, Phys. Rev. E, 68, 056110, 10.1103/PhysRevE.68.056110

2008, Cluster analysis for portfolio optimization, J. Econ. Dyn. Control, 32, 235, 10.1016/j.jedc.2007.01.034

2016, A network approach to portfolio selection, J. Empir. Finance, 38, 157, 10.1016/j.jempfin.2016.06.003

2014, Systemic risk and spatiotemporal dynamics of the US housing market, Sci. Rep., 4, 3655, 10.1038/srep03655

2004, Networks of equities in financial markets, Eur. Phys. J. B, 38, 363, 10.1140/epjb/e2004-00129-6

2014, Stock network stability in times of crisis, Phys. A—Stat. Mech. Appl., 393, 376, 10.1016/j.physa.2013.08.053

2018, Predicting economic growth with stock networks, Phys. A—Stat. Mech. Appl., 489, 102, 10.1016/j.physa.2017.07.022

1998, Collective dynamics of ‘small-world’ networks, Nature, 393, 440, 10.1038/30918

2012, Small-world topology of functional connectivity in randomly connected dynamical systems, Chaos, 22, 033107, 10.1063/1.4732541

2016, Beware of the small-world neuroscientist!, Front. Hum. Neurosci., 10, 96, 10.3389/fnhum.2016.00096

2017, Small-world bias of correlation networks: From brain to climate, Chaos, 27, 035812, 10.1063/1.4977951

2006, What do networks have to do with climate?, Bull. Am. Meteorol. Soc., 87, 585, 10.1175/BAMS-87-5-585

2015, Graph theory in the geosciences, Earth Sci. Rev., 143, 147, 10.1016/j.earscirev.2015.02.002

2008, Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain, NeuroImage, 43, 528, 10.1016/j.neuroimage.2008.08.010

2007, Correlation based networks of equity returns sampled at different time horizons, Eur. Phys. J. B, 55, 209, 10.1140/epjb/e2006-00414-4

2017, The predictive power of local properties of financial networks, Phys. A—Stat. Mech. Appl., 466, 79, 10.1016/j.physa.2016.08.032

1994, Functional, effective connectivity in neuroimaging: A synthesis, Hum. Brain Mapp., 2, 56, 10.1002/hbm.460020107

2004, The architecture of the climate network, Phys. A—Stat. Mech. Appl., 333, 497, 10.1016/j.physa.2003.10.045

2005, Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field, Clin. Neurophysiol., 116, 2266, 10.1016/j.clinph.2005.06.011

2011, Functional connectivity in resting-state FMRI: Is linear correlation sufficient?, NeuroImage, 54, 2218, 10.1016/j.neuroimage.2010.08.042

2011, The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks, Chaos, 21, 013119, 10.1063/1.3553181

2014, Non-linear dependence and teleconnections in climate data: Sources, relevance, nonstationarity, Clim. Dyn., 42, 1873, 10.1007/s00382-013-1780-2

2013, Reliability of inference of directed climate networks using conditional mutual information, Entropy, 15, 2023, 10.3390/e15062023

2014, Networks in financial markets based on the mutual information rate, Phys. Rev. E, 89, 052801, 10.1103/PhysRevE.89.052801

See http://www.nyse.com/ for more information about New York Stock Exchange—NYSE (2017); accessed 20 July 2017.

2017, Emerging interdependence between stock values during financial crashes, PLoS One, 12, e0176764, 10.1371/journal.pone.0176764

See http://www.ftse.com for more information about FTSE group (2017); accessed 15 June 2017.

2015, Eccentricity in asset management, Netw. Theory Finance, 1, 1, 10.21314/JNTF.2015.003

2017, Interconnectedness risk and active portfolio management, J. Invest. Strateg., 6, 63, 10.21314/JOIS.2017.081

2017, Interconnectedness risk and active portfolio management: The information-theoretic perspective

See https://finance.yahoo.com/ for more information about Yahoo! finance (2017); accessed 15 August 2017.

See http://www.spindices.com/ for more information about S&p Dow Jones indices (2017); accessed 10 July 2017.

Kadtke, 1997, Degree of correlation inside a financial market, Applied Nonlinear Dynamics and Stochastic Systems Near the Millennium, 197

1993, Information theoretic test for nonlinearity in time-series, Phys. Lett. A, 175, 203, 10.1016/0375-9601(93)90827-M

Serguieva, 2014, Frequency effects on predictability of stock returns, 247

Brabazon, 2008, On predictability and profitability: Would GP induced trading rules be sensitive to the observed entropy of time series?,, 197

1995, Testing for nonlinearity using redundancies—Quantitative and qualitative aspects, Phys. D—Nonlinear Phenom., 80, 186, 10.1016/0167-2789(95)90079-9

2005, A tool for filtering information in complex systems, Proc. Natl. Acad. Sci. USA., 102, 10421, 10.1073/pnas.0500298102

2010, A network perspective of the stock market, J. Empir. Finance, 17, 659, 10.1016/j.jempfin.2010.04.008

2010, Correlation structure and dynamics in volatile markets, New J. Phys., 12, 085009, 10.1088/1367-2630/12/8/085009

2004, Clustering and information in correlation based financial networks, Eur. Phys. J. B, 38, 353, 10.1140/epjb/e2004-00128-7

2005, Statistical analysis of financial networks, Comput. Stat. Data Anal., 48, 431, 10.1016/j.csda.2004.02.004

2009, A network analysis of the Chinese stock market, Phys. A—Stat. Mech. Appl., 388, 2956, 10.1016/j.physa.2009.03.028

2015, Unveiling correlations between financial variables and topological metrics of trading networks: Evidence from a stock and its warrant, Phys. A: Stat. Mech. Appl., 419, 575, 10.1016/j.physa.2014.10.039

1999, Emergence of scaling in random networks, Science, 286, 509, 10.1126/science.286.5439.509

1987, Power and centrality—A family of measures, Am. J. Sociol., 92, 1170, 10.1086/228631

2003, Mixing patterns in networks, Phys. Rev. E, 67, 026126, 10.1103/PhysRevE.67.026126

1994, Generating surrogate data for time-series with several simultaneously measured variables, Phys. Rev. Lett., 73, 951, 10.1103/PhysRevLett.73.951

1997, Detecting phase synchronization in noisy systems, Phys. Lett. A, 235, 341, 10.1016/S0375-9601(97)00635-X

2011, Discerning connectivity from dynamics in climate networks, Nonlinear Process. Geophys., 18, 751, 10.5194/npg-18-751-2011

2004, Estimating mutual information, Phys. Rev. E, 69, 066138, 10.1103/PhysRevE.69.066138

1995, Estimation of mutual information using kernel density estimators, Phys. Rev. E, 52, 2318, 10.1103/PhysRevE.52.2318

2016, Complex network analysis of time series, Europhys. Lett., 116, 50001, 10.1209/0295-5075/116/50001

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Tập 28 Số 8

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