Black Swans, Dragons-Kings and Prediction
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Power-Law Distributions in Empirical Data
Power-law distributions in empirical data Aaron Clauset,1, 2 Cosma Rohilla Shalizi,3 and M. E. J. Newman1, 4 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA 2Department of Computer Science, University of New Mexico, Albuquerque, NM 87131, USA 3Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 4Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA Power-law distributions occur in many situations of scientific interest and have significant conse- quences for our understanding of natural and man-made phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we review statistical techniques for making ac- curate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law dis- tribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twenty- four real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out. -
From Big Data to Econophysics and Its Use to Explain Complex Phenomena
Journal of Risk and Financial Management Review From Big Data to Econophysics and Its Use to Explain Complex Phenomena Paulo Ferreira 1,2,3,* , Éder J.A.L. Pereira 4,5 and Hernane B.B. Pereira 4,6 1 VALORIZA—Research Center for Endogenous Resource Valorization, 7300-555 Portalegre, Portugal 2 Department of Economic Sciences and Organizations, Instituto Politécnico de Portalegre, 7300-555 Portalegre, Portugal 3 Centro de Estudos e Formação Avançada em Gestão e Economia, Instituto de Investigação e Formação Avançada, Universidade de Évora, Largo dos Colegiais 2, 7000 Évora, Portugal 4 Programa de Modelagem Computacional, SENAI Cimatec, Av. Orlando Gomes 1845, 41 650-010 Salvador, BA, Brazil; [email protected] (É.J.A.L.P.); [email protected] (H.B.B.P.) 5 Instituto Federal do Maranhão, 65075-441 São Luís-MA, Brazil 6 Universidade do Estado da Bahia, 41 150-000 Salvador, BA, Brazil * Correspondence: [email protected] Received: 5 June 2020; Accepted: 10 July 2020; Published: 13 July 2020 Abstract: Big data has become a very frequent research topic, due to the increase in data availability. In this introductory paper, we make the linkage between the use of big data and Econophysics, a research field which uses a large amount of data and deals with complex systems. Different approaches such as power laws and complex networks are discussed, as possible frameworks to analyze complex phenomena that could be studied using Econophysics and resorting to big data. Keywords: big data; complexity; networks; stock markets; power laws 1. Introduction Big data has become a very popular expression in recent years, related to the advance of technology which allows, on the one hand, the recovery of a great amount of data, and on the other hand, the analysis of that data, benefiting from the increasing computational capacity of devices. -
Didier Sornette Curriculum Vitae Born in Paris, France, 25 June 1957
Didier Sornette Curriculum Vitae Born in Paris, France, 25 June 1957, maried, two sons. Graduate from Ecole Normale Superieure (ENS Ulm, Paris), in Physical Sciences (1977-81) Research scientist of the CNRS (French National Center for Scientific Research) (1981-1990) PhD at University of Nice on Statistical Physics of interfaces (1985) Research director at CNRS, France, since oct. 1990 Professor at UCLA, California (1996-2006) Professor on the Chair of Entrepreneurial Risks at ETH-Zurich (since March 2006) Concurrent Professor of East China University of Science and Technology (ECUST), Shanghai, China, since May 2004. First SAG Visiting Professor at the Washington University in St. Louis, St. Louis, Missouri, USA; Systems Analysis Group (SAG) (http://cia.wustl.edu/SAG/people.shtml) (2005-present) Director of Research in the X-RS research & development company in Orsay, France (1988-1995) Scientific advisor of the technical director of Thomson-Marconi Sonar company (now THALES) in Nice-Sophia Antipolis Technopolis, France (1984-1996) Advisor of aerospace industrial companies, banks, investment and reinsurance companies (1991-present). Science et Defence French National Award (1985) 2000 Research McDonnell award: Studying Complex Systems, the Scientific Prediction of Crises Risques-Les Echos prize 2002 for Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth Elected Fellow of the World Innovation Foundation (WIF) (6th February 2004) Invited foreign participant to the Center of Excellence Project, Japan on ``Interfaces of Advanced Economic Analysis'', Kyoto University, Graduate School of Economics, Faculty of Economics, Kyoto, Japan (since April, 2004) Member of the Global Advisory Board of Human Dignity and Humiliation Studies (http://www.humiliationstudies.org/) Associate Editor for the journal of Quantitative Finance (2001-present); member of the editorial board of the International Journal of Modern Physics C (computational physics) (2005-present). -
Market Crash Prediction Model for Markets in a Rational Bubble
Market Crash Prediction Model for Markets in A Rational Bubble HyeonJun Kim UG in Dept.Finance, Soongsil University [email protected] August 27, 2021 Abstract Renowned method of log-periodic power law(LPPL) is one of the few ways that a financial market crash could be predicted. Alongside with LPPL, this paper propose a novel method of stock market crash using white box model derived from simple assumptions about the state of rational bubble. By applying this model to Dow Jones Index and Bitcoin market price data, it is shown that the model successfully predicts some major crashes of both markets, implying the high sensitivity and generalization abilities of the model. keywords: [Rational Bubble], [Market Crash] 1 Introduction It is well known that the efficient market price tends to follow the characteristics of Brownian Motionthat strictly depends on stochastic nature[3]. Thus predicting the information about the short-term return of a financial portfolio is known to be difficult, but there are few exceptions. Firstly, there is a widely heldbelief among traders that it is possible for some computational deterministic patterns to emerge for short period of time. This belief, combined with econophysics, led the creation of algorithmic trading funds such as Prediction Company and Renaissance Technologies. Secondly, there is a concept of rational bubble that illustrates the rational behavior of people who invest in markets that clearly creating an economic bubble[1]. With these two facts in mind, it is possible to imagine a model with reasonable assumptions to predict rational bubble's key behaviors, such as the stock market crash after a bubble economy. -
Emergent Properties & Security
Emergent Properties & Security: The Complexity of Security as a Science Nathaniel Husted Steven Myers School of Informatics and Computing School of Informatics and Computing Indiana University Indiana University ABSTRACT Emergent properties are now well studied in a large num- The notion of emergent properties is becoming common place ber of scientific and social scientific fields, spanning from in the physical and social sciences, with applications in physics, from biology to sociology. Examples here include ant colonies chemistry, biology, medicine, economics, and sociology. Un- that are seen as having properties that are independent of fortunately, little attention has been given to the discussion individual ants to human culture [31]. While there have of emergence in the realm of computer security, from either been some calls for its study by academics in the popular the attack or defense perspectives, despite there being ex- press [27], the academic study of emergence in information amples of such attacks and defenses. We review the concept security has mostly been restricted to isolated cases, rarely of emergence, discuss it in the context of computer security, with a view on reflecting on the broader picture of the pos- argue that understanding such concepts is essential for se- sibilities of emergent vulnerabilities, attacks, defenses and curing our current and future systems, give examples of cur- diagnostics. rent attacks and defenses that make use of such concepts, Recently there has been much interest in the science of se- and discuss the tools currently available to understand this curity [55]. The goal of the science of security is to develop field. -
Time-Varying Volatility and the Power Law Distribution of Stock Returns
Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Time-varying Volatility and the Power Law Distribution of Stock Returns Missaka Warusawitharana 2016-022 Please cite this paper as: Warusawitharana, Missaka (2016). “Time-varying Volatility and the Power Law Distribution of Stock Returns,” Finance and Economics Discussion Se- ries 2016-022. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2016.022. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Time-varying Volatility and the Power Law Distribution of Stock Returns Missaka Warusawitharana∗ Board of Governors of the Federal Reserve System March 18, 2016 JEL Classifications: C58, D30, G12 Keywords: Tail distributions, high frequency returns, power laws, time-varying volatility ∗I thank Yacine A¨ıt-Sahalia, Dobislav Dobrev, Joshua Gallin, Tugkan Tuzun, Toni Whited, Jonathan Wright, Yesol Yeh and seminar participants at the Federal Reserve Board for helpful comments on the paper. Contact: Division of Research and Statistics, Board of Governors of the Federal Reserve System, Mail Stop 97, 20th and C Street NW, Washington, D.C. 20551. [email protected], (202)452-3461. -