Efficient Parameter-Estimating Algorithms for Symmetry-Motivated Models: Econometrics and Beyond

  • Vladik Kreinovich
  • Anh H. Ly
  • Olga Kosheleva
  • Songsak Sriboonchitta
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 760)


It is known that symmetry ideas can explain the empirical success of many non-linear models. This explanation makes these models theoretically justified and thus, more reliable. However, the models remain non-linear and thus, identification or the model’s parameters based on the observations remains a computationally expensive nonlinear optimization problem. In this paper, we show that symmetry ideas can not only help to select and justify a nonlinear model, they can also help us design computationally efficient almost-linear algorithms for identifying the model’s parameters.



We acknowledge the partial support of the Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Thailand. This work was also supported in part by the National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence).


  1. 1.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)zbMATHGoogle Scholar
  2. 2.
    Feigenbaum, J.A.: A statistical analyses of log-periodic precursors to financial crashes. Quant. Financ. 1(5), 527–532 (2001)CrossRefGoogle Scholar
  3. 3.
    Feigenbaum, J.A., Freund, P.: Discrete scaling in stock markets before crashes. Int. J. Mod. Phys. 12, 57–60 (1996)zbMATHGoogle Scholar
  4. 4.
    Gazola, L., Fenandez, C., Pizzinga, A., Riera, R.: The log-periodic-AR (1)-GARCH (1,1) model for financial crashes. Eur. Phys. J. B 61(3), 355–362 (2008)CrossRefzbMATHGoogle Scholar
  5. 5.
    Geraskin, P., Fantazzinin, D.: Everything you always wanted to know about log periodic power laws for bubble modelling but were afraid to ask. Eur. J. Financ. 19(5), 366–391 (2013)CrossRefGoogle Scholar
  6. 6.
    Goodfellow, I., Bengio, Y., Courville, A.: Deep Leaning. MIT Press, Cambridge (2016)zbMATHGoogle Scholar
  7. 7.
    Jiang, Z.Q., Zhou, W.H., Sornette, D., Woodard, R., Bastiaensen, K., Cauwels, P.: Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles. J. Econ. Behav. Organ. 74, 149–162 (2010)CrossRefGoogle Scholar
  8. 8.
    Johansen, A.: Characterization of large price variations in financial markets. Phys. A 324, 157–166 (2003)CrossRefzbMATHGoogle Scholar
  9. 9.
    Johansen, A., Ledoit, O., Sornette, D.: Crashes as critical points. Int. J. Theor. Appl. Financ. 3(2), 219–255 (2000)CrossRefzbMATHGoogle Scholar
  10. 10.
    Johansen, A., Sornette, D.: Financial anti-bubbles: log-periodicity in Gold and Nikkei collapses. Int. J. Mod. Phys. C 10(4), 563–575 (1999)CrossRefGoogle Scholar
  11. 11.
    Johansen, A., Sornette, D.: Large stock market price drawdowns are outliers. J. Risk 4(2), 69–110 (2002)CrossRefGoogle Scholar
  12. 12.
    Johansen, A., Sornette, D.: Endogenous versus exogenous crashes in financial markets. In: Contemporary Issues in International Finance. Nova Science Publishers (2004). Reprinted as a special issue of Brussels Economic Review, vol. 49, No. 3/4 2006Google Scholar
  13. 13.
    Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1998)CrossRefzbMATHGoogle Scholar
  14. 14.
    Kreinovich, V., Nguyen, H.T., Sriboonchitta, S.: Log-periodic power law as a predictor of catastrophic events: a new mathematical justification. In: Proceedings of the International Conference on Risk Analysis in Meteorological Disasters, RAMD 2014, Nanjing, China, 12–13 October 2014 (2014)Google Scholar
  15. 15.
    Kreinovich, V., Swenson, T., Elentukh, A.: Interval approach to testing software. Interval Comput. 2, 90–109 (1994)Google Scholar
  16. 16.
    Nguyen, H.T., Kreinovich, V.: Applications of Continuous Mathematics to Computer Science. Kluwer, Dordrecht (1997)CrossRefzbMATHGoogle Scholar
  17. 17.
    Papadimitriou, C.H.: Computational Complexity. Pearson, Boston (1993)zbMATHGoogle Scholar
  18. 18.
    Pardalos, P.: Complexity in Numerical Optimization. World Scientific, Singapore (1993)CrossRefzbMATHGoogle Scholar
  19. 19.
    Poole, D.: Linear Algebra: A Modern Introduction. Cengage Learning, Independence (2014)Google Scholar
  20. 20.
    Robinson, J.C.: An Introduction to Ordinary Differential Equations. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  21. 21.
    Sornette, D.: Critical market crashes. Phys. Rep. 378(1), 1–98 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Sornette, D.: Why Stock Markets Crash: Critical Events in Compelx Financial Systems. Princeton University Press, Princeton (2003)zbMATHGoogle Scholar
  23. 23.
    Sornette, D., Johansen, A.: Significance of log-periodic precursors to financial crashes. Quant. Financ. 1(4), 452–471 (2001)CrossRefGoogle Scholar
  24. 24.
    Sornette, D., Zhou, W.Z.: The US 2000–2002 market descent: how much longer and deeper? Quant. Financ. 2(6), 468–481 (2002)Google Scholar
  25. 25.
    Weatherall, J.M.: The Physics of Wall Street: The History of Predicting the Unpredictable. Houghton Mifflin Harcourt, New York (2013)Google Scholar
  26. 26.
    Zhou, W.Z., Sornette, D.: Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000. Phys. A 330(3), 543–583 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vladik Kreinovich
    • 1
  • Anh H. Ly
    • 2
  • Olga Kosheleva
    • 1
  • Songsak Sriboonchitta
    • 3
  1. 1.University of Texas at El PasoEl PasoUSA
  2. 2.Banking University of Ho Chi Minh CityHo Ch Minh CityVietnam
  3. 3.Faculty of EconomicsChiang Mai UniversityChiang MaiThailand

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