Abstract
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.
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References
M. Bordo, Unpublished manuscript, Rutgers University (2003)
D. Rapp, Bubbles, booms, and busts: The Rise and Fall of Financial Assets (Springer-Verlag, 2009)
G. Caginalp, D. Porter, V. Smith, J. Behav. Finance 2, 80 (2001)
D. Porter, V. Smith, J. Behav. Finance 4, 7 (2003)
E. Majorana, Scientia 36, 58 (1942)
W. Arthur, Am. Econ. Rev. 84, 406 (1994)
D. Sornette, A. Johansen, J.P. Bouchaud, J. Phys. I 6, 167 (1996)
D. Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton University Press, 2004)
E. Zababakhin, J. Exp. Theoret. Phys. 49, 642 (1965)
E. Novikov, Phys. Fluids A 2, 814 (1990)
G. Jona-Lasinio, Nuovo Cim. B 26, 99 (1975)
M.E. Nauenberg, J. Phys. A 8, 925 (1975)
J. Anifrani, C. Le Floc’h, D. Sornette, B. Souillard, J. Phys. I 5, 631 (1995)
A. Johansen, D. Sornette, Eur. Phys. J. B 18, 163 (2000)
J. Kwapień, S. Drożdż, Phys. Rep. 515, 115 (2012)
D. Sornette et al., J. Phys. I 5, 607 (1995)
H. Saleur et al., Nonlin. Proc. Geophys. 3, 102 (1996)
H. Saleur, C. Sammis, D. Sornette, J. Geophys. Res. 101, 17661 (1996)
L. Gazola, C. Fernandes, A. Pizzinga, R. Riera, Eur. Phys. J. B 61, 355 (2008)
O. Blanchard, Econ. Lett. 3, 387 (1979)
J.A. Feigenbaum, P.G. Freund, Int. J. Mod. Phys. B 10, 3737 (1996)
D. Sornette, A. Johansen, Physica A 245, 411 (1997)
A. Johansen, D. Sornette, Risk 12, 91 (1999)
A. Johansen, D. Sornette, O. Ledoit, J. Risk 1, 5 (1999)
A. Johansen, O. Ledoit, D. Sornette, Int. J. Theor. Appl. Finance 3, 219 (2000)
A. Johansen, D. Sornette, Int. J. Mod. Phys. C 10, 563 (1999)
A. Johansen, D. Sornette, Eur. Phys. J. B 17, 319 (2000)
D. Sornette, W.X. Zhou, Quant. Finance 2, 468 (2002)
D. Fantazzini, Econ. Bull. 30, 1833 (2010)
D. Sornette, R. Woodard, W.X. Zhou, Physica A 388, 1571 (2009)
Z.Q. Jiang, W.X. Zhou, D. Sornette, R. Woodard, K. Bastiaensen, P. Cauwels, J. Econ. Behav. Organiz. 74, 149 (2010)
P. Geraskin, D. Fantazzini, Eur. J. Finance 19, 366 (2013)
P. Gnaciński, D. Makowiec, Physica A 344, 322 (2004)
S. Drozdz, J. Kwapien, P. Oswiecimka, J. Speth, Acta Phys. Polon. A 114, 539 (2008)
D. Fantazzini, in The Handbook of Trading: Strategies for Navigating and Profiting from Currency, Bond, and Stock Markets (McGraw-Hall, 2010), p. 365
W.X. Zhou, D. Sornette, Physica A 388, 869 (2009)
F. Busetti, The Effective Investor: Lessons from an African Emerging Markets (MacMillan, 2009)
A. Johansen, D. Sornette, Int. J. Theor. Appl. Finance 4, 853 (2001)
J.R. Kurz-Kim, Appl. Econ. Lett. 19, 1465 (2012)
R. Matsushita, S. Da Silva, Econ. Bull. 31, 1772 (2011)
D. Fantazzini, Econ. Bull. 31, 3259 (2011)
J.A. Feigenbaum, Quant. Finance 1, 527 (2001)
D. Sornette et al., Quant. Finance 1, 452 (2001)
J.A. Feigenbaum, Quant. Finance 1, 346 (2001)
V. Liberatore, arXiv:1003.2920 (2010)
D.S. Brée, D. Challet, P.P. Peirano, Quant. Finance 13, 275 (2013)
D. Sornette, R. Woodard, W. Yan, W.X. Zhou, Physica A 392, 4417 (2013)
G. Chang, J. Feigenbaum, Quant. Finance 6, 15 (2006)
D. Gamerman, H.F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (Chapman and Hall, 1997)
G. Casella, E.I. George, Am. Statistician 46, 167 (1992)
S. Chib, E. Greenberg, Am. Statistician 49, 327 (1995)
G. Casella, M. Lavine, C.P. Robert, Am. Statistician 55, 299 (2001)
L. Ingber, Math. Comput. Modell. 12, 967 (1989)
H. Haario, E. Saksman, J. Tamminen, Bernoulli 7, 223 (2001)
A. Villagran et al., Bayesian Analysis 3, 823 (2008)
S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220, 671 (1983)
A. Villagran, G. Huerta, Adv. Econometrics 20, 277 (2006)
M. Kozlowska, R. Kutner, Acta Phys. Polon. B 37, 3027 (2006)
M. Kozłowska, A. Kasprzak, R. Kutner, Int. J. Mod. Phys. C 19, 453 (2008)
M. Bartolozzi, S. Drożdż, D.B. Leinweber, J. Speth, A.W. Thomas, Int. J. Mod. Phys. C 16, 1347 (2005)
D. Ventosa-Santaulària, J. Probab. Statistics 2009, 802975 (2009)
P.C.B. Phillips, J. Yu, Quant. Econ. 2, 455 (2011)
P. Phillips, S.P. Shi, J. Yu, Cowles Foundation Discussion Paper (2012)
P.C.B. Phillips, S. Shi, J. Yu, Oxford Bull. Econ. Statist. 76, 315 (2014)
P.C.B. Phillips, Y. Wu, J. Yu, Int. Econ. Rev. 52, 201 (2011)
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Rodríguez-Caballero, C., Knapik, O. Bayesian log-periodic model for financial crashes. Eur. Phys. J. B 87, 228 (2014). https://doi.org/10.1140/epjb/e2014-41085-6
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DOI: https://doi.org/10.1140/epjb/e2014-41085-6