Analysis of precursory and aftershock properties of shocks and ruptures in finance, material rupture, earthquakes, amazon.com sales, etc: we find ubiquitous power laws similar to the Omori law in seismology that allow us to distinguish between external shocks and endogenous self-organization.
Self-organized criticality, and more generally, complex system theory contend that out-of-equilibrium slowly driven systems with threshold dynamics relax through a hierarchy of avalanches of all sizes. Accordingly, extreme events are seen to be endogenous, in contrast with previous prevailing views. But, how can one assert with 100% confidence that a given extreme event is really due to an endogenous self-organization of the system, rather than to the response to an external shock? Most natural and social systems are indeed continuously subjected to external stimulations, noises, shocks, sollications, forcing, which can widely vary in amplitude. It is thus not clear a priori if a given large event is due to a strong exogenous shock, to the internal dynamics of the system, or maybe to a combination of both. Adressing this question is fundamental for understanding the relative importance of self-organization versus external forcing in complex systems.
This question, whether distinguishing properties characterize endogenous versus exogenous shocks, permeates many systems, for instance, biological extinctions such as the Cretaceous/Tertiary KT boundary (meteorite versus extreme volcanic activity versus self-organized critical extinction cascades), commercial successes (progressive reputation cascade versus the result of a well orchestrated advertisement), immune system deficiencies (external viral/bacterial infections versus internal cascades of regulatory breakdowns), the aviation industry recession (9/11 versus structural endogenous problems), discoveries (serendipity versus the outcome of slow endogenous maturation processes), cognition and brain learning processes (role of external inputs versus internal self-organization and reinforcements) and recovery after wars (internally generated (civil wars) versus imported from the outside) and so on. In economics, endogeneity versus exogeneity has been hotly debated for decades. A prominent example is the theory of Schumpeter on the importance of technological discontinuities in economic history. Schumpeter argued that ``evolution is lopsided, discontinuous, disharmonious by nature... studded with violent outbursts and catastrophes... more like a series of explosions than a gentle, though incessant, transformation''. Endogeneity versus exogeneity is also paramount in economic growth theory. Our analysis suggests a subtle interplay between exogenous and endogenous shocks which casts a new light on this debate.
We study the precursory and recovery signatures accompanying shocks in complex networks, that we have tested on a unique database of the Amazon sales ranking of books and on time series of financial volatility. We find clear distinguishing signatures classifying two types of sales peaks. Exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous sales peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks. These results are rationalized quantitatively by a simple model of epidemic propagation of interactions with long memory within a network of acquaintances in the case of the Amazon data and by the ``multifractal random walk'' model in the case of the financial volatility time series. The slow relaxation of sales implies that the sales dynamics is dominated by cascades rather than by the direct effects of news or advertisements, indicating that the social network is close to critical.
APPLICATION TO BOOK SALES ON AMAZON
D. Sornette, F. Deschatres, T. Gilbert and Y. Ageon, Endogenous Versus Exogenous Shocks in Complex Networks: an Empirical Test Using Book Sale Ranking, Phys. Rev. Letts. 93 (22), 228701 (2004)
F. Deschatres and D. Sornette, The Dynamics of Book Sales: Endogenous versus Exogenous Shocks in Complex Networks, Phys. Rev. E 72, 016112 (2005)
APPLICATION TO LONG MEMORY IN FINANCIAL VOLATILITY
D. Sornette, Y. Malevergne and J.-F. Muzy, What causes crashes? (This paper could be called: "Omori's law for aftershocks in finance'' or "Volatility fingerprints of large shocks: Endogenous versus exogenous'') Risk 16 (2), 67-71 (February 2003). Are large market events caused by exogenous shocks or can they occur endogenously? Here, the authors ask this question of large stock market events and conclude that endogenous crashes do exist.
D. Sornette, Y. Malevergne and J.-F. Muzy, Volatility Fingerprints of Large Shocks: Endogenous Versus Exogenous, in "Application of Econophysics, "Proceedings of the second Nikkei symposium on econophysics, H. Takayasu, ed., Springer Verlag, ISBN 4.431-14028-X, 334 p. 137 illus. (2004)
APPLICATION TO FINANCIAL CRASHES
A. Johansen and D. Sornette, Shocks, Crashes and Bubbles in Financial Markets, Brussels Economic Review (Cahiers economiques de Bruxelles), 49 (3/4), Special Issue on Nonlinear Analysis (2006)
D. Sornette Why Stock Markets Crash (Critical Events in Complex Financial Systems) Princeton University Press, January 2003
G. Harras and D. Sornette, Endogenous versus exogenous origins of financial rallies and crashes in an agent-based model with Bayesian learning and imitation, submitted to J. Economic Behavior and Organization (2008)
(http://arXiv.org/abs/0806.2989) and (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1156348)
GENERAL FORMALISM AND LINKS BETWEEN EXOGENOUS AND ENDOGENOUS RESPONSES TO SHOCKS (a kind of generalization to the "fluctuation-susceptibility" theorem)
D. Sornette and A. Helmstetter Endogenous Versus Exogenous Shocks in Systems with Memory, Physica A 318, 577 (15 Feb 2003)
D. Sornette and S. Utkin, Limits of Declustering Methods for Disentangling Exogenous from Endogenous Events in Time Series with Foreshocks, Main shocks and Aftershocks, Physical Review E 79, 061110 (2009)
A. Saichev and D. Sornette, Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes, European Physical Journal B 75, 343-355 (2010)
APPLICATIONS TO EARTHQUAKES
A. Helmstetter, D. Sornette and J.-R. Grasso, Mainshocks are Aftershocks of Conditional Foreshocks: How do foreshock statistical properties emerge from aftershock laws, J. Geophys. Res., 108 (B10), 2046, doi:10.1029/2002JB001991, (2003).
APPLICATION TO OTHER SOCIAL SYSTEMS, INTERNET NETWORKS, SOCIAL CRISES
B.M. Roehner, D. Sornette and J.V. Andersen, Response Functions to
Critical Shocks in Social Sciences: An Empirical and Numerical Study,
Int. J. Mod. Phys. C 15 (6), 809-834 (2004)
D. Sornette, Endogenous versus exogenous origins of crises, in monograph entitled "Extreme Events in Nature and Society", Series: The Frontiers Collection S. Albeverio, V. Jentsch and H Kantz, eds. (Springer, Heidelberg, 2005) pp 95-119
R. Crane and D. Sornette, Robust dynamic classes revealed by measuring the response function of a social system, Prod. Nat. Acad. Sci. USA 105 (41), 15649-15653 (2008)
(http://arxiv.org/abs/0412026) Media coverage: ETH-life / TagesAnzeiger
R. Crane, F. Schweitzer and D. Sornette, New Power Law Signature of Media Exposure in Human Response Waiting Time Distributions, Physical Review E 81, 056101 (2010)
by Joseph Lopez
A book bought, red, treasured, reread and at a later date, passed on, or sadly thrown away. Ultimately, the lifespan or life service of a publication depends on the patron. Some books never die; the best example is the Bible, which has been printed more than six billion times. Why do some books "live"longer?
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