“Speculative Influence Network” during financial bubbles: application to Chinese stock markets

  • Li Lin
  • Didier Sornette
Regular Article


We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion and a bubble regime represented by the stochastic super-exponential Sornette and Andersen (Int J Mod Phys C 13(2):171–188, 2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset i onto another asset j, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005–2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity variable as the difference between the transfer entropies from i to j and from j to i, which is used in a series of rank ordered regressions to predict the maximum loss (%MaxLoss) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is some predictability obtained by using the transfer entropy involving industrial sectors to explain the %MaxLoss of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.


Financial bubbles Super-exponential Systemic risks Hidden Markov Modeling Transfer entropy Speculative Influence Network Early warning system Chinese stock market 

JEL Classification

C46 D85 G01 G17 



We acknowledge financial support from the National Natural Science Founds of China (Grant No. 71301051) and the Fundamental Research Funds for the Central Universities of China (Grant No.  WN1522007).


  1. Acemoglu D, Ozdaglar A, Tahbaz-Salehi A (2015) Systemic risk and stability in financial networks. Am Econ Rev 105(2):564–608CrossRefGoogle Scholar
  2. Allen F, Babus A (2009) Ch in finance. In: The network challenge: strategy, profit, and risk in an interlinked world. Networks, Pearson Prentice HallGoogle Scholar
  3. Ancona N, Marinazzo D, Stramaglia S (2004) Radial basis function approach to nonlinear granger causality of time series. Phys Rev E 70(5):0562211:1–0562211:7CrossRefGoogle Scholar
  4. Andersen J, Sornette D (2004) Fearless versus fearful speculative financial bubbles. Phys A 337(3–4):565–585CrossRefGoogle Scholar
  5. Anufriev M, Panchenko V (2015) Connecting the dots: econometric methods for uncovering networks with an application to the australian financial institutions. J Bank Finance 61:S241–S255CrossRefGoogle Scholar
  6. Ardila-Alvarez D, Forró Z, Sornette D, (2015) The acceleration effect and gamma factor in asset pricing. Swiss Finance Institute Research Paper No. 15-30. Available at SSRN:
  7. Avery C, Zemsky P (1998) Multidimensional uncertainty and herd behavior in financial markets. Am Econ Rev 88(4):724–748Google Scholar
  8. Banerjee AV (1992) A simple model of herd behavior. Q J Econ 107(3):797–817CrossRefGoogle Scholar
  9. Barberis N, Shleifer A, Vishny R (1998) A model of investor sentiment. J Financ Econ 49(3):307–343CrossRefGoogle Scholar
  10. Barnett L, Barrett AB, Seth AK (2009) Granger causality and transfer entropy are equivalent for Gaussian variables. Phys Rev Lett 103(23):238701CrossRefGoogle Scholar
  11. Barrett AB, Barnett L (2013) Granger causality is designed to measure effect, not mechanism. Front Neuroinform 7(6):1–2Google Scholar
  12. Bikhchandani S, Hirshleifer D, Welch I (1992) A theory of fads, fashion, custom, and cultural change as informational cascades. J Polit Econ 100(5):992–1026CrossRefGoogle Scholar
  13. Billio M, Getmansky M, Lo AW, Pelizzon L (2012) Econometric measures of connectedness and systemic risk in the finance and insurance sectors. J Financ Econ 104(3):535–559CrossRefGoogle Scholar
  14. Brunnermeier M K, Oehmke M (2013) Bubbles, financial crises, and systemic risk. Handbook of the Economics of Finance. Elsevier 2 (B), AmsterdamGoogle Scholar
  15. Cajueiro D, Tabak B, Werneck F (2009) Can we predict crashes? The case of the Brazilian stock market. Phys A 388(8):1603–1609CrossRefGoogle Scholar
  16. Chiang TC, Li J, Tan L (2010) Empirical investigation of herding behavior in chinese stock markets: evidence from quantile regression analysis. Glob Finance J 21(1):111–124CrossRefGoogle Scholar
  17. Chincarini L B (2012) The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal. Wiley, New YorkCrossRefGoogle Scholar
  18. Choi N, Sias RW (2009) Institutional industry herding. J Financ Econ 94(3):469–491CrossRefGoogle Scholar
  19. Dass N, Massa M, Patgiri R (2008) Mutual funds and bubbles: the surprising role of contractual incentives. Rev Financ Stud 21(1):51–99CrossRefGoogle Scholar
  20. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodol) 39(1):1–38Google Scholar
  21. Devenow A, Welch I (1996) Rational herding in financial economics. Eur Econ Rev 40(3):603–615CrossRefGoogle Scholar
  22. Diks C, Panchenko V (2006) A new statistic and practical guidelines for nonparametric granger causality testing. J Econ Dyn Control 30(9):1647–1669CrossRefGoogle Scholar
  23. Dimitriadi G (2004) What are ”financial bubbles”: approaches and definitions. Electronic Journal “INVESTIGATED in RUSSIA”Google Scholar
  24. Filimonov V, Sornette D (2013) A stable and robust calibration scheme of the log-periodic power law model. Phys A Stat Mech Appl 392(17):3698–3707CrossRefGoogle Scholar
  25. Francis BB, Mougoué M, Panchenko V (2010) Is there a symmetric nonlinear causal relationship between large and small firms? J Empir Finance 17(1):23–38CrossRefGoogle Scholar
  26. Giordano M, Mannella R (2006) A brief analysis of May 2004 crash in the indian market. Fluct Noise Lett 6(3):243–249CrossRefGoogle Scholar
  27. Gisler M, Sornette D, Woodard R (2011) Innovation as a social bubble: the example of the human genome project. Res Policy 40:1412–1425CrossRefGoogle Scholar
  28. Gurkaynak RS (2008) Econometric tests of asset price bubbles: taking stock. J Econ Surv 22(1):166–186CrossRefGoogle Scholar
  29. Hamilton JD (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econom J Econom Soc 57(2):357–384Google Scholar
  30. He Z, Su D (2009) Price manipulation and industry momentum: evidence from the chinese stock market. Available at SSRN:
  31. Hlavácková-Schindler K (2011) Equivalence of granger causality and transfer entropy: a generalization. Appl Math Sci 5(73):3637–3648Google Scholar
  32. Hong H, Kubik JD, Stein JC (2005) Thy neighbor’s portfolio: word-of-mouth effects in the holdings and trades of money managers. J Finance 60(6):2801–2824CrossRefGoogle Scholar
  33. Hüsler A, Sornette D, Hommes CH (2013) Super-exponential bubbles in lab experiments: evidence for anchoring over-optimistic expectations on price. J Econ Behav Organ 92:304–316CrossRefGoogle Scholar
  34. Ide K, Sornette D (2002) Oscillatory finite-time singularities in finance, population and rupture. Phys A 307(1–2):63–106CrossRefGoogle Scholar
  35. Jeanblanc M, Yor M, Chesney M (2009) Mathematical methods for financial markets. Springer Finance Textbooks, Springer Finance, BerlinCrossRefGoogle Scholar
  36. Jiang Z-Q, Zhou W-X, Sornette D, Woodard R, Bastiaensen K, Cauwels P (2010) Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 chinese stock market bubbles. J Econ Behav Organ 74(3):149–162CrossRefGoogle Scholar
  37. Johansen A, Ledoit O, Sornette D (2000) Crashes as critical points. Int J Theor Appl Finance 3:219–255Google Scholar
  38. Johansen A, Sornette D (2000) The nasdaq crash of April 2000: yet another example of log-perodicity in a speculative bubble ending in a crash. Eur Phys J B 17:319–328CrossRefGoogle Scholar
  39. Johansen A, Sornette D (2001) Bubbles and anti-bubbles in latin-american, asian and western stock markets: an empirical study. Int J Theor Appl Finance 4(6):853–920CrossRefGoogle Scholar
  40. Johansen A, Sornette D, Ledoit O (1999) Predicting financial crashes using discrete scale invariance. J Risk 1(4):5–32CrossRefGoogle Scholar
  41. Kaizoji T, Leiss M, Saichev A, Sornette D (2015) Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders. J Econ Behav Organ 112:289–310CrossRefGoogle Scholar
  42. Khwaja AI, Mian A (2005) Unchecked intermediaries: price manipulation in an emerging stock market. J Financ Econ 78(1):203–241CrossRefGoogle Scholar
  43. Kim C-J, Nelson CR (1999) State-space models with regime switching. MIT Press, CambridgeGoogle Scholar
  44. Lakonishok J, Shleifer A, Vishny RW (1994) Contrarian investment, extrapolation, and risk. J Finance 49(5):1541–1578CrossRefGoogle Scholar
  45. Leiss M, Nax H, Sornette D (2015) Super-exponential growth expectations and the global financial crisis. J Econ Dyn Control 55:1–13CrossRefGoogle Scholar
  46. Li W, Rhee G, Wang SS (2009) Differences in herding: individual vs. institutional investors in china. Institutional Investors in China (SSRN: February 13, 2009)Google Scholar
  47. Lin L, Ren R-E, Sornette D (2014) The volatility-confined LPPL model: a consistent model of ‘explosive’financial bubbles with mean-reverting residuals. Int Rev Financ Anal 33:210–225CrossRefGoogle Scholar
  48. Lin L, Sornette D (2013) Diagnostics of rational expectation financial bubbles with stochastic mean-reverting termination times. Eur J Finance 19(5):344–365CrossRefGoogle Scholar
  49. Long JBD, Shleifer A, Summers LH, Waldmann RJ (1990) Noise trader risk in financial markets. J Polit Econ 98(4):703–738CrossRefGoogle Scholar
  50. Lungarella M, Ishiguro K, Kuniyoshi Y, Otsu N (2007) Methods for quantifying the causal structure of bivariate time series. Int J Bifurc Chaos 17(03):903–921CrossRefGoogle Scholar
  51. Matsushita R, da Silva S, Figueiredo A, Gleria I (2006) Log-periodic crashes revisited. Phys A 364:331–335CrossRefGoogle Scholar
  52. Nofsinger JR, Sias RW (1999) Herding and feedback trading by institutional and individual investors. J Finance 54(6):2263–2295CrossRefGoogle Scholar
  53. Piotroski JD, Wong T (2011) Institutions and information environment of Chinese listed firms. In: Capitalizing China. University of Chicago Press, pp 201–242Google Scholar
  54. Redner S (2001) A guide to first-passage processes. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  55. Roehner BM, Sornette D (2000) ”Thermometers” of speculative frenzy. Eur Phys J B Condens Matter 16(4):729–739Google Scholar
  56. Schreiber T (2000) Measuring information transfer. Phys Rev Lett 85(2):461–464CrossRefGoogle Scholar
  57. Shiller RJ (2000) Irrational exuberance. Princeton University Press, PrincetonGoogle Scholar
  58. Sias RW (2004) Institutional herding. Rev Financ Stud 17(1):165–206CrossRefGoogle Scholar
  59. Sornette D (1998) Discrete-scale invariance and complex dimensions. Phys Rep 297:239–270CrossRefGoogle Scholar
  60. Sornette D, Andersen JV (2002) A nonlinear super-exponential rational model of speculative financial bubbles. Int J Mod Phys C 13(2):171–188CrossRefGoogle Scholar
  61. Sornette D, Cauwels P (2014) 1980–2008: The illusion of the perpetual money machine and what it bodes for the future. Risks 2:103–131CrossRefGoogle Scholar
  62. Sornette D, Cauwels P (2015) Financial bubbles: mechanisms and diagnostics. Rev Behav Econ 2(3).
  63. Sornette D, Demos G, Zhang Q, Cauwels P, Filimonov V, Zhang Q (2015) Real-time prediction and post-mortem analysis of the Shanghai 2015 stock market bubble and crash. J Invest Strateg 4(4):77–95CrossRefGoogle Scholar
  64. Sornette D, Johansen A (1998) A hierarchical model of financial crashes. Phys A Stat Mech Appl 261:581–598CrossRefGoogle Scholar
  65. Sornette D, Woodard R, (2010) Financial bubbles, real estate bubbles, derivative bubbles, and the financial and economic crisis. In: Takayasu M, Watanabe T, Takayasu H (eds) Proceedings of APFA7 (Applications of Physics in Financial Analysis), “New Approaches to the Analysis of Large-Scale Business and Economic Data”. Springer, Berlin. arXiv:0905.0220
  66. Sornette D, Woodard R, Zhou WX (2009) The 2006–2008 oil bubble: evidence of speculation, and prediction. Phys A 388:1571–1576CrossRefGoogle Scholar
  67. Sornette D, Zhou W-X (2006) Predictability of large future changes in major financial indices. Int J Forecast 22:153–168CrossRefGoogle Scholar
  68. Tan L, Chiang TC, Mason JR, Nelling E (2008) Herding behavior in chinese stock markets: an examination of a and b shares. Pac Basin Finance J 16(1):61–77CrossRefGoogle Scholar
  69. Xu N-X, Yu S-R, Yin ZH (2013) Institutional investor herding and stock price crash risk. Manag World (Chinese) 7:31–43Google Scholar
  70. Zhou CS, Yang YH, Wang Y-P (2005) Trading-based market manipulation in china’s stock market. Econ Res J (in Chinese) 10:70–78Google Scholar
  71. Zhou W X, Sornette D (2006) Fundamental factors versus herding in the 2000–2005 us stock market and prediction. Phys A Stat Mech Appl 360(2):459–482CrossRefGoogle Scholar
  72. Zhou WX, Sornette D (2006b) Is there a real-estate bubble in the us? Phys A Stat Mech Appl 361(1):297–308CrossRefGoogle Scholar
  73. Zhou W-X, Sornette D (2008) Analysis of the real estate market in las vegas: bubble, seasonal patterns, and prediction of the csw indexes. Phys A 387:243–260CrossRefGoogle Scholar
  74. Zhou W-X, Sornette D (2009) A case study of speculative financial bubbles in the South African stock market 2003–2006. Phys A 388:869–880CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of BusinessEast China University of Technology and ScienceShanghaiChina
  2. 2.Department of Management, Technology and EconomicsETH ZurichZurichSwitzerland
  3. 3.Swiss Finance Institute, c/o University of GenevaGeneva 4Switzerland
  4. 4.Research Institute of Financial EngineeringEast China University of Technology and ScienceShanghaiChina

Personalised recommendations