Abstract
This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.
Similar content being viewed by others
References
M. Takayasu, T. Watanabe, H. Takayasu, J. Stat. Phys. 138, 431 (2010)
T. Preis, H.E. Stanley, J. Stat. Phys. 138, 431 (2010)
Google Corporation, http://www.google.de/trends, April 2010
T. Preis, D. Reith, H.E. Stanley, Philosoph. Trans. Royal Soc. A 368, 5707 (2010)
M.F.M. Osborne, Oper. Res. 7, 145 (1959)
M.F.M. Osborne, The Stock Market and Finance from a Physicist’s Viewpoint (Crossgar Press, 1995)
B. Mandelbrot, J. Business 36, 394 (1963)
K. Kiyono, Z.R. Struzik, Y. Yamamoto, Physical Rev. Lett. 96, 068701 (2006)
J.-P. Bouchaud, M. Potters, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, 2nd edn. (Cambridge University Press, 2009)
R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, 2000)
W. Paul, J. Baschnagel, Stochastic Processes: From Physics to Finance (Springer, 2000)
Deutsche Börse Systems expands ultra low latency network, Press Release, Deutsche Börse AG, January 2010
L. Bachelier, Théorie de la Spéculation, Ph.D. thesis (Faculté des Sciences de Paris, 1900)
A. Einstein, Ann. Phys. 17, 549 (1905)
E. Ising, Z. Phys. 31, 253 (1925)
L. Onsager, Phys. Rev. 65, 117 (1944)
J.J. Schneider, S. Kirkpatrick, Stochastic Optimization (Springer, 2006)
S. Moss de Oliveira, P.M.C. de Oliveira, D. Stauffer, Evolution, Money, War, and Computers (Teubner, 1999)
K. Sznajd-Weron, J. Sznajd, Int. J. Modern Phys. C 11, 1157 (2000)
K. Nagel, M. Schreckenberg, J. Phys. I (France) 2, 2221 (1992)
D. Helbing, Phys. Rev. E 55, R25 (1997)
D. Brockmann, L. Hufnagel, T. Geisel, Nature 439, 462 (2006)
J.-M. Courtault, Y. Kabanov, B. Bru, P. Crépel, I. Lebon, A. Le Marchand, Math. Finance 10, 341 (2000)
F. Black, M. Scholes, J. Political Econ. 81, 637 (1973)
R.C. Merton, Bell J. Econom. Manag. Sci. 4, 141 (1973)
P. Bank, D. Baum, Math. Finance 14, 1 (2004)
T. Preis, Eur. Phys. J. Special Topics 194, 87 (2011)
P. Bak, M. Paczuski, M. Shubik, Physica A 246, 430 (1997)
S. Maslov, Physica A 278, 571 (2000)
S. Maslov, M. Mills, Physica A 299, 234 (2001)
D. Challet, R. Stinchcombe, Quant. Finance 3, 155 (2003)
D. Stauffer, D. Sornette, Physica A 271, 496 (1999)
T. Lux, M. Marchesi, Nature 397, 498 (1999)
A. Krawiecki, J.A. Holyst, D. Helbing, Phys. Rev. Lett. 89, 158701 (2002)
G. Caldarelli, M. Marsili, Y.-C. Zhang, Europhys. Lett. 40, 479 (1997)
M.G. Daniels, J.D. Farmer, L. Gillemot, G. Iori, E. Smith, Phys. Rev. Lett. 90, 108102 (2003)
E. Smith, J.D. Farmer, L. Gillemot, S. Krishnamurthy, Quant. Finance 3, 481 (2003)
P.W. Andersen, Science 177, 393 (1972)
H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, 1971)
R.L. Axtell, Science 293, 1818 (2001)
H. Takayasu (ed.), Practical Fruits of Econophysics (Springer, 2006)
K. Watanabe, H. Takayasu, M. Takayasu, Physica A 383, 120 (2007)
X. Gabaix, P. Gopikrishnan, V. Plerou, H.E. Stanley, Nature 423, 267 (2003)
T. Preis, W. Paul, J.J. Schneider, Europhys. Lett. 82, 68005 (2008)
F. Lillo, J.D. Farmer, R.N. Mantegna, Nature 421, 129 (2003)
V. Plerou, P. Gopikrishnan, X. Gabaix, H.E. Stanley, Phys. Rev. E 66, 027104 (2002)
R. Cont, J.-P. Bouchaud, Macroeconom. Dyn. 4, 170 (2000)
M. O’Hara, Market Microstructure Theory (Blackwell Publishing, 1997)
N. Vandewalle, M. Ausloos, Physica A 246, 454 (1997)
Z. Eisler, J. Kertész, Phys. Rev. E 73, 046109 (2006)
E.F. Fama, J. Business 36, 420 (1963)
T. Lux, Appl. Financial Econom. 6, 463 (1996)
D.M. Guillaume, M.M. Dacorogna, R.R. Davé, U.A. Müller, R.B. Olsen, O.V. Pictet, Finance Stoch. 1, 95 (1997)
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley, Phys. Rev. Lett. 83, 1471 (1999)
T. Preis, Investigation of a multi-agent based order book model of financial markets (Diploma thesis, 2006)
T. Preis, S. Golke, W. Paul, J.J. Schneider, Europhys. Lett. 75, 510 (2006)
U. Krengel, Einführung in die Wahrscheinlichkeitstheorie und Statistik (Vieweg, 2003)
R. Dubil, An Arbitrage Guide to Financial Markets (Wiley, 2004)
R. Cont, Quant. Finance 1, 223 (2001)
T. Preis, Ökonophysik: Die Physik des Finanzmarktes, 1st edn. (Gabler, Wiesbaden, 2011)
H.-P. Deutsch, Derivate und Interne Modelle. Modernes Risikomanagement. (Schäffer-Poeschel, 2003)
P.M. Garber, J. Political Econ. 97, 535 (1989)
P.M. Garber, Famous First Bubbles: The Fundamentals of Early Manias (MIT Press, 2000)
A. Goldgar, Tulipmania: Money, Honor, and Knowledge in the Dutch Golden Age (University of Chicago Press, 2007)
S. Trautmann, Investitionen. Bewertung, Auswahl und Risikomanagement (Springer, 2006)
Annual Report 2005 (Deutsche Börse Group, 2006)
N. Kuls, Das New Yorker Börsenparkett schrumpft auf die Hälfte. (Frankfurter Allgemeine Zeitung, 2007)
J. Anderson, U.S. proposes ban on ’flash’ trading on wall street. (New York Times, 2009)
P. Gopikrishnan, V. Plerou, L.A.N. Amaral, M. Meyer, H.E. Stanley, Phys. Rev. E 60, 5305 (1999)
J.-P. Bouchaud, M. Potters, Physica A 299, 60 (2001)
D. Stauffer, T.J.P. Penna, Physica A 256, 284 (1998)
T. Preis, S. Golke, W. Paul, J.J. Schneider, Phys. Rev. E 76, 016108 (2007)
L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters, Phys. Rev. Lett. 83, 1467 (1999)
A.G. Zawadowski, J. Kertész, G. Andor, Physica A 344, 221 (2004)
A.G. Zawadowski, G. Andor, J. Kertész, Quant. Finance 6, 283 (2006)
A. Alfonsi, A. Fruth, A. Schied, Quant. Finance 10, 143 (2009)
B. Biais, P. Hillion, C. Spatt, J. Finance 50, 1655 (1995)
M.K. Brunnermeier, L.H. Pedersen, J. Finance 60, 1825 (2005)
D. Bertsimas, A.W. Lo, J. Financial Mark. 1, 1 (1998)
T. Preis, P. Virnau, W. Paul, J.J. Schneider, New J. Phys. 11, 093024 (2009)
H.E. Hurst, Trans. Amer. Soc. Civil Eng. 116, 770 (1951)
G.A. Darbellay, D. Wuertz, Physica A 287, 429 (2000)
M. Ausloos, Physica A 285, 48 (2000)
A. Carbone, G. Castelli, H.E. Stanley, Physica A 344, 267 (2004)
D.P. Landau K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 2nd edn. (Cambridge University Press, 2005)
D. Reith, P. Virnau, Comp. Phys. Comm. 181, 800 (2010)
T. Preis, P. Virnau, W. Paul, J.J. Schneider, J. Comput. Phys. 228, 4468 (2009)
B. Block, P. Virnau, T. Preis, Comput. Phys. Commun. 181, 1549 (2010)
C.H. Hommes, Proc. Nation. Acad. Sci. 99, 7221 (2002)
W.T. Shaw, J. Comput. Finance 9, 37 (2006)
P.R. Hansen, J. Large, A. Lunde, Econom. Rev. 27, 79 (2008)
W. Haerdle, T. Kleinow, A. Korostelev, C. Logeay, E. Platen, Quant. Finance 8, 81 (2008)
A.D. Hall, N. Hautsch, J. Financial Mark. 10, 249 (2007)
C. Jones, G. Kaul, M. Lipson, Rev. Financial Stud. 7, 631 (1994)
K. Chan, W.-M. Fong, J. Financial Econom. 57, 247 (2000)
M. Politi, E. Scalas, Physica A 387, 2025 (2008)
Z.-Q. Jiang, W. Chen, W.-X. Zhou, Physica A 388, 433 (2009)
P.C. Ivanov, A. Yuen, B. Podobnik, Y. Lee, Phys. Rev. E 69, 056107 (2004)
P. Krugman, The Self-Organizing Economy (Wiley-Blackwell, 1996)
A. Shleifer, Inefficient Markets: An Introduction to Behavioral Finance (Oxford University Press, 2000)
D. Helbing, I. Farkas, T. Vicsek, Nature 407, 487 (2000)
A. Bunde, J. Kropp, H.J. Schellnhuber (eds.), The Science of Disaster: Climate Disruptions, Market Crashes, and Heart Attacks (Springer, 2002)
H.E. Stanley, S.V. Buldyrev, G. Franzese, S. Havlin, F. Mallamace, P. Kumar, V. Plerou, T. Preis, Physica A 389, 2880 (2010)
A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. (Cambridge University Press, 1992)
D.J. Bennett, Randomness (Harvard University Press, 1998)
K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369, 343 (2006)
J.L. McCauley, G.H. Gunaratne, K.E. Bassler, Physica A 379, 1 (2007)
M. Pasquini, M. Serva, Econom. Lett. 65, 275 (1999)
M. Serva, U.L. Fulco, I.M. Gléria, M.L. Lyra, F. Petroni, G.M. Viswanathan, Physica A 363, 393 (2006)
M. Wyart, J.-P. Bouchaud, J. Kockelkoren, M. Potters, M. Vettorazzo, Quant. Finance 8, 41 (2008)
J. Voit, The Statistical Mechanics of Financial Markets (Springer, 2005)
R.N. Mantegna, H.E. Stanley, Phys. Rev. Lett. 73, 2946 (1994)
I. Koponen, Phys. Rev. E 52, 1197 (1995)
G.M. Viswanathan, U.L. Fulco, M.L. Lyra, M. Serva, Physica A 329, 273 (2003)
R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)
T. Preis, J. Phys.: Conf. Ser. 221, 012019 (2010)
T. Preis, Quantifying, modeling financial market fluctuations, Ph.D. thesis (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Preis, T. Econophysics — complex correlations and trend switchings in financial time series. Eur. Phys. J. Spec. Top. 194, 5–86 (2011). https://doi.org/10.1140/epjst/e2011-01397-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2011-01397-y