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Dragon-Kings the Nature of Extremes, StaSCal Tools of Outlier DetecOn, GeneraNg Mechanisms, PredicOn and Control Didier SORNETTE Professor Of

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Dragon-Kings the Nature of Extremes, Sta�S�Cal Tools of Outlier Detec�On, Genera�Ng Mechanisms, Predic�On and Control Didier SORNETTE Professor Of Zurich Dragon-Kings the nature of extremes, sta4s4cal tools of outlier detec4on, genera4ng mechanisms, predic4on and control Didier SORNETTE Professor of Professor of Finance at the Swiss Finance Institute associated with the Department of Earth Sciences (D-ERWD), ETH Zurich associated with the Department of Physics (D-PHYS), ETH Zurich Director of the Financial Crisis Observatory Founding member of the Risk Center at ETH Zurich (June 2011) (www.riskcenter.ethz.ch) Black Swan (Cygnus atratus) www.er.ethz.ch Fundamental changes follow extremes • Droughts and the collapse of the Mayas (760-930 CE) • French revolution 1789 • “Spanish” worldwide flu 1918 • USSR collapse 1991 • Challenger space shuttle disaster 1986 • dotcom crash 2000 • Financial crisis 2008 • Next financial-economic crisis? • European sovereign debt crisis: Brexit… Grexit…? • Next cyber-collapse? • “Latent-liability” and extreme events 23 June 2016 How Europe fell out of love with the EU ! What is the nature of extremes? Are they “unknown unknowns”? ? Black Swan (Cygnus atratus) 32 Standard view: fat tails, heavy tails and Power law distributions const −1 ccdf (S) = 10 complementary cumulative µ −2 S 10 distribution function 10−3 10−4 10−5 10−6 10−7 102 103 104 105 106 107 Heavy tails in debris Heavy tails in AE before rupture Heavy-tail of pdf of war sizes Heavy-tail of cdf of cyber risks ID Thefts MECHANISMS -proportional growth with repulsion from origin FOR POWER LAWS -proportional growth birth and death processes -coherent noise mechanism Mitzenmacher M (2004) A brief history of generative -highly optimized tolerant (HOT) systems models for power law and lognormal distributions, Internet Mathematics 1, -sandpile models and threshold dynamics 226-251. (self-organized criticality => fault and earthquakes) Newman MEJ (2005) Power •critical desynchronization laws, Pareto distributions and •dynamical system theory of self-organized criticality Zipf’s law, Contemporary (coupling of sub-critical bifurcations) Physics 46, 323-351. D. Sornette (2004) Probability -nonlinear feedback of the order parameter onto the control parameter Distributions in Complex Systems, Encyclopedia of Complexity and System -generic scale invariance Science (Springer Science), 2004 -mapping onto a critical point (contact processes) D. Sornette (2006) Critical Phenomena in Natural Sciences, Chaos, Fractals, -extremal dynamics Self-organization and Disorder: Concepts and Tools, -sweeping of an instability 2nd ed., 2nd print, pp.528, 102 const figs. , 4 tabs (Springer Series ccdf (S) = µ in Synergetics, Heidelberg) -avalanches in hysteretic loops S Power law-Black Swan story • Unknown unknowable event ★ cannot be diagnosed in advance, cannot be quantified, no predictability • No responsability (“wrath of God”) • Standard approach: statistical risk and reliability analysis Proposition: Extremes and Crises are not black swans but “Dragon-kings” Dragon-kings (DK) embody a double metaphor implying that an event is both extremely large (a "king''), and born of unique origins ("dragon") relative to its peers. The hypothesis proposed in [Sornette, 2009] is that DK events are generated by distinct mechanisms that intermittently amplify extreme events, leading to the generation of runaway disasters as well as extraordinaryBlack Swan (Cygnus opportunities atratus) on the upside. Beyond power laws: examples of “Dragons” Financial economics: Outliers and dragons in the distribution of financial drawdowns. Population geography: Paris as the dragon-king in the Zipf distribution of French city sizes. Material science: failure and rupture processes. Hydrodynamics: Extreme dragon events in the pdf of turbulent velocity fluctuations. Metastable states in random media: Self-organized critical random directed polymers Brain medicine: Epileptic seizures Geophysics: Characteristic earthquakes? Great avalanches? Floods? Mountain collapses? Meteological events? and so on Ionosphere and magneto-hydrodynamics: Global auroral energy deposition 2009 dragon-kings (Spencer Wheatley and Didier Sornette, 2015) time-to-failure analysis ... H. Nechad, A. Helmstetter, R. El Guerjouma and D. Sornette, Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model, Journal of Mechanics and Physics of Solids (JMPS) 53, 1099-1127 (2005) Energy distribution for the [+-62] specimen #4 at different times, for 5 time windows with 3400 events each. The average time (in seconds) of events in each window is given in the caption. S.G. Sammis and D. Sornette, Positive Feedback, Memory and the Predictability of Earthquakes, Proceedings of the National Academy of Sciences USA, V99 SUPP1:2501-2508 (2002 FEB 19) Cumulative probability distribution of epidemic fatalities amplification by (i) hiding and (ii) enhanced connectivity via WWII 1918 spanish flu dragon-kings source: http://www.emdat.be Traditional emphasis on Daily returns do not reveal any anomalous events 42 (Courtesy Vladimir Filimonov) Most extremes are dragon-kings Better risk measure: drawdowns A. Johansen and D. Sornette, Stock market crashes are outliers, European Physical Journal B 1, 141-143 (1998) A. Johansen and D. Sornette, Large Stock Market Price Drawdowns Are Outliers, Journal of Risk 4(2), 69-110, Winter 2001/02 43 Extreme Risks: Dragon-Kings versus Black Swans Special Issue EPJ ST SPRINGER D. Sornette and G. Ouillon Guest Editors (May 2012) Dragon-king hypothesis • Most crises and extremes are “endogenous” ★ can be diagnosed in advance, can be quantified, (some) predictability • Moral hazard, conflict of interest, role of regulations • Responsibility, accountability • Strategic vs tactical time- dependent strategy • Weak versus global signals POSITIVE FEEDBACKS http://www.businessweek.com/the_thread/economicsunbound/archives/2009/03/a_bad_decade_fo.html Michael Mandel Ex. of Dragon-King: the 2008 crisis Index of over- • Worldwide bubble (1980-Oct. 1987) valuation • The ICT (dotcom) “new economy” bubble (1995-2000) • Real-estate bubbles (2003-2006) • MBS, CDOs bubble (2004-2007) • Stock market bubble (2004-2007) • Commodities and Oil bubbles (2006-2008) • Debt bubbles The “perpetual money machine” broke. PCA first component on a data set containing, emerging markets equity indices, freight indices, soft commodities, base and precious metals, energy, currencies... 2003 2004 2005 2006 2007 2008 2009 D. Sornette and P. Cauwels, 1980-2008: The Illusion of the Perpetual Money Machine and what it bodes for the future, Risks 2, 103-131 (2014) (http://arxiv.org/abs/1212.2833) THE GREAT MODERATION source: U.S. Bureau of Labor Statistics. Wheatley, Spencer and Sornette, Didier (2016) Test statistics for DK detection sum to robust-sum statistic: max to robust-sum statistic: issues of (i) swamping vs masking; (ii) inward vs outward Wheatley, Spencer and Sornette, Didier (2016) MRS: Max-Robust-Sum ratio; SRS: Sum-Robust-Sum ratio Wheatley, Spencer and Sornette, Didier (2016) Wheatley, Spencer and Sornette, Didier (2016) (NAMS: Nuclear Accident Magnitude Scale) CCDF of severity of events. Panel I: The main frame plots the cost of events for the pre- and post- TMI periods according to their CCDFs, in gray and black, respectively. The lower inset figure shows the p-value of a segmentation test of the cost data, identifying TMI (1979) as the change-point in the cost distribution. The upper inset figure shows the estimated parameter α (with standard deviation) of a Pareto distribution (Equation (3)), for the post-TMI cost data, for a range of lower thresholds (u1). The fit for u1 = 30 (MM USD) is given by the red solid line in the main frame. Panel II: In the main frame, from left to right, are the CCDF of INES scores above 2 (shifted left by 1), the CCDF of NAMS scores above 2, and the CCDF of the natural logarithm of post-1980 costs (shifted right by 2). For the center and right CCDFs, the dots with x marks indicate suspected outliers/dragon kings. The dashed and solid red lines are exponential fits to the CCDFs. The inset figure provides the p- value for the outlier test for the upper sample above a growing threshold. The upper curve is for r = 3 outliers, and the lower curve for r = 2 outliers. Spencer Wheatley, Benjamin Sovacool and Didier Sornette, Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents & Accidents, Risk Analysis DOI: 10.1111/risa.12587, pp. 1-17 (2016) DK-detection by breakdown of collapse of pdf’s at different scales Pdf of the square of the Velocity as in the previous figure but for a much longer time series, so that the tail of the distributions for large Fluctuations is much better constrained. The hypothesis that there are no outliers is tested here by collapsing the Collapse ~of positions and amplitudes for five intensive peaks belonging to the 20th shell. distributions for the three shown layers. While this is a success for small fluctuations, the tails of the distributions for large events are very different, indicating that extreme fluctuations belong to a different class of their own and hence are outliers. L'vov, V.S., Pomyalov, A. and Procaccia, I. (2001) Outliers, Extreme Events and Multiscaling, Physical Review E 6305 (5), 6118, U158-U166. Mechanisms for Dragon-kings •Partial global synchronization •Generalized correlated (droplets) percolation •Transient positive feedbacks leading to singular “finite-time singularity” and changes of regimes/ ruptures/phase transitions •A kind of condensation (a la Bose-Einstein) •Forward looking optimisation of consumption/ investment in economic models with heterogenous
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