arXiv subjects

Didier Sornette

Publications and source records attributed to Didier Sornette.

At least 199 records · Page 11Linked to original sources

arXiv2009

Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking

We model the progressive maturation of a heterogeneous mass towards a gravity-driven instability, characterized by the competition between frictional sliding and tension cracking, using array of slider blocks on an inclined basal surface, which interact via elastic-brittle springs. A realistic state- and rate-dependent friction law describes the block-surface interaction. The inner material damage occurs via stress corrosion. Three regimes, controlling the mass instability and its precursory behavior, are classified as a function of the ratio $T_c/T_f$ of two characteristic time scales associated with internal damage/creep and with frictional sliding. For $T_c/T_f \gg 1$, the whole mass undergoes a series of internal stick and slip events, associated with an initial slow average downward motion of the whole mass, and progressively accelerates until a global coherent runaway is observed. For $T_c/T_f \ll 1$, creep/damage occurs sufficiently fast compared with nucleation of sliding, causing bonds to break, and the bottom part of the mass undergoes a fragmentation process with the creation of a heterogeneous population of sliding blocks. For the intermediate regime $T_c/T_f \sim 1$, a macroscopic crack nucleates and propagates along the location of the largest curvature associated with the change of slope from the stable frictional state in the upper part to the unstable frictional sliding state in the lower part. The other important parameter is the Young modulus $Y$ which controls the correlation length of displacements in the system.

physics.geo-ph↗

arXiv2008

Look-Ahead Benchmark Bias in Portfolio Performance Evaluation

Performance of investment managers are evaluated in comparison with benchmarks, such as financial indices. Due to the operational constraint that most professional databases do not track the change of constitution of benchmark portfolios, standard tests of performance suffer from the "look-ahead benchmark bias," when they use the assets constituting the benchmarks of reference at the end of the testing period, rather than at the beginning of the period. Here, we report that the "look-ahead benchmark bias" can exhibit a surprisingly large amplitude for portfolios of common stocks (up to 8% annum for the S&P500 taken as the benchmark) -- while most studies have emphasized related survival biases in performance of mutual and hedge funds for which the biases can be expected to be even larger. We use the CRSP database from 1926 to 2006 and analyze the running top 500 US capitalizations to demonstrate that this bias can account for a gross overestimation of performance metrics such as the Sharpe ratio as well as an underestimation of risk, as measured for instance by peak-to-valley drawdowns. We demonstrate the presence of a significant bias in the estimation of the survival and look-ahead biases studied in the literature. A general methodology to test the properties of investment strategies is advanced in terms of random strategies with similar investment constraints.

q-fin.PM↗

arXiv2008

A case study of speculative financial bubbles in the South African stock market 2003-2006

We tested 45 indices and common stocks traded in the South African stock market for the possible existence of a bubble over the period from Jan. 2003 to May 2006. A bubble is defined by a faster-than-exponential acceleration with significant log-periodic oscillations. The faster-than-exponential acceleration characteristics are tested with several different metrics, including nonlinearity on the logarithm of the price and power law fits. The log-periodic properties are investigated in detail using the first-order log-periodic power-law (LPPL) formula, the parametric detrending method, the $(H,q)$-analysis, and the second-order Weierstrass-type model, resulting in a consistent and robust estimation of the fundamental angular log-frequency $ω_1 =7\pm 2$, in reasonable agreement with previous estimations on many other bubbles in developed and developing markets. Sensitivity tests of the estimated critical times and of the angular log-frequency are performed by varying the first date and the last date of the stock price time series. These tests show that the estimated parameters are robust. With the insight of 6 additional month of data since the analysis was performed, we observe that many of the stocks on the South Africa market experienced an abrupt drop mid-June 2006, which is compatible with the predicted $t_c$ for several of the stocks, but not all. This suggests that the mini-crash that occurred around mid-June of 2006 was only a partial correction, which has resumed into a renewed bubbly acceleration bound to end some times in 2007, similarly to what happened on the S&P500 US market from Oct. 1997 to Aug. 1998.

physics.soc-ph↗

arXiv2008

"Bubbles in Society": The Example of the United States Apollo Program

We present an analysis of the economic, political and social factors that underlay the Apollo program, one of the most exceptional and costly projects ever undertaken by the United States in peacetime that culminated in 1969 with the first human steps on the Moon. This study suggests that the Apollo program provides a vivid illustration of a societal bubble, defined as a collective over-enthusiasm as well as unreasonable investments and efforts, derived through excessive public and/or political expectations of positive outcomes associated with a general reduction of risk aversion. We show that economic, political and social factors weaved a network of reinforcing feedbacks that led to widespread over-enthusiasm and extraordinary commitment by individuals involved in the project as well as by politicians and by the public at large. We propose the general concept of ``pro-bubbles,'' according to which bubbles are an unavoidable development in technological and social enterprise that benefits society by allowing exceptional niches of innovation to be explored.

physics.soc-ph↗

arXiv2008

Novel insights into the dynamics of intractable human epilepsy

Probability density functions and the probability of Sz occurrence conditional upon the time elapsed from the previous Sz were estimated using the energy and intervals of SZ in prolonged recordings from subjects with localization- related pharmaco-resistant epilepsy, undergoing surgical evaluation. Clinical and subclinical seizure E and ISI distributions are governed by power laws in subjects on reduced doses of anti-seizure drugs. There is increased probability of Sz occurrence 30 minutes before and after a seizure and the time to next seizure increases with the duration of the seizure-free interval since the last one. Also, over short time scales, ``seizures may beget seizures.'' The cumulative empirical evidence is compatible with and suggests that at least over short time scales, seizures have the inherent capacity of triggering other seizures. This may explain the tendency of seizures to cluster and evolve into status epilepticus. Power law distributions of E and ISI indicate these features lack a typical size/duration and may not be accurate criteria or sufficient for classifying paroxysmal activity as ictal or interictal. This dependency and the existence of power law distributions raise the possibility that Sz occurrence and intensity may be predictable, without specifying the likelihood of success.

q-bio.NC↗

arXiv2007

Epileptic Seizures: Quakes of the brain?

The concept of universality proposes that dynamical systems with the same power law behaviors are equivalent at large scales. We test this hypothesis on the Earth's crust and the epileptic brain, and discover that power laws also govern the distributions of seizure energies and recurrence times. This robust correspondence is extended over seven statistics, including the direct and inverse Omori laws. We also verify in an animal seizure model the earthquake-driven hypothesis that power law statistics co-exist with characteristic scales, as coupling between constitutive elements increases towards the synchronization regime. These observations point to the universality of the dynamics of coupled threshold oscillators for systems even as diverse as Earth and brain and suggest a general strategy for forecasting seizures, one of neurosciences' grails.

physics.bio-ph↗

arXiv2007

A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics

Validation is often defined as the process of determining the degree to which a model is an accurate representation of the real world from the perspective of its intended uses. Validation is crucial as industries and governments depend increasingly on predictions by computer models to justify their decisions. In this article, we survey the model validation literature and propose to formulate validation as an iterative construction process that mimics the process occurring implicitly in the minds of scientists. We thus offer a formal representation of the progressive build-up of trust in the model, and thereby replace incapacitating claims on the impossibility of validating a given model by an adaptive process of constructive approximation. This approach is better adapted to the fuzzy, coarse-grained nature of validation. Our procedure factors in the degree of redundancy versus novelty of the experiments used for validation as well as the degree to which the model predicts the observations. We illustrate the new methodology first with the maturation of Quantum Mechanics as the arguably best established physics theory and then with several concrete examples drawn from some of our primary scientific interests: a cellular automaton model for earthquakes, an anomalous diffusion model for solar radiation transport in the cloudy atmosphere, and a computational fluid dynamics code for the Richtmyer-Meshkov instability. This article is an augmented version of Sornette et al. [2007] that appeared in Proceedings of the National Academy of Sciences in 2007 (doi: 10.1073/pnas.0611677104), with an electronic supplement at URL http://www.pnas.org/cgi/content/full/0611677104/DC1. Sornette et al. [2007] is also available in preprint form at physics/0511219.

physics.comp-ph↗

arXiv2007

Nurturing Breakthroughs: Lessons from Complexity Theory

A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by ubiquitous ``bubbles'', which involve huge risks which would not otherwise be taken using standard cost/benefit analysis. Bubbles result from self-reinforcing positive feedbacks. This leads to explore uncharted territories and niches whose rare successes lead to extraordinary discoveries and provide the base for the observed accelerating development of technology and of the economy. But the returns are very heterogeneous, very risky and may not occur. In other words, bubbles, which are characteristic definitions of human activity, allow huge risks to get huge returns over large scales. We outline some underlying mathematical structure and a few results involving positive feedbacks, emergence, heavy-tailed power laws, outliers/kings/black swans, the problem of predictability and the illusion of control, as well as some policy implications.

physics.soc-ph↗

arXiv2007

Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indexes

We analyze 27 house price indexes of Las Vegas from Jun. 1983 to Mar. 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real-estate bubble, defined as a price acceleration faster than exponential, which is found however to be confined to a rather limited time interval in the recent past from approximately 2003 to mid-2004 and has progressively transformed into a more normal growth rate comparable to pre-bubble levels in 2005. There has been no bubble till 2002 except for a medium-sized surge in 1990. In addition, we have identified a strong yearly periodicity which provides a good potential for fine-tuned prediction from month to month. A monthly monitoring using a model that we have developed could confirm, by testing the intra-year structure, if indeed the market has returned to ``normal'' or if more turbulence is expected ahead. We predict the evolution of the indexes one year ahead, which is validated with new data up to Sep. 2006. The present analysis demonstrates the existence of very significant variations at the local scale, in the sense that the bubble in Las Vegas seems to have preceded the more global USA bubble and has ended approximately two years earlier (mid 2004 for Las Vegas compared with mid-2006 for the whole of the USA).

q-fin.GN↗

arXiv2007

Automatic Reconstruction of Fault Networks from Seismicity Catalogs: 3D Optimal Anisotropic Dynamic Clustering

We propose a new pattern recognition method that is able to reconstruct the 3D structure of the active part of a fault network using the spatial location of earthquakes. The method is a generalization of the so-called dynamic clustering method, that originally partitions a set of datapoints into clusters, using a global minimization criterion over the spatial inertia of those clusters. The new method improves on it by taking into account the full spatial inertia tensor of each cluster, in order to partition the dataset into fault-like, anisotropic clusters. Given a catalog of seismic events, the output is the optimal set of plane segments that fits the spatial structure of the data. Each plane segment is fully characterized by its location, size and orientation. The main tunable parameter is the accuracy of the earthquake localizations, which fixes the resolution, i.e. the residual variance of the fit. The resolution determines the number of fault segments needed to describe the earthquake catalog, the better the resolution, the finer the structure of the reconstructed fault segments. The algorithm reconstructs successfully the fault segments of synthetic earthquake catalogs. Applied to the real catalog constituted of a subset of the aftershocks sequence of the 28th June 1992 Landers earthquake in Southern California, the reconstructed plane segments fully agree with faults already known on geological maps, or with blind faults that appear quite obvious on longer-term catalogs. Future improvements of the method are discussed, as well as its potential use in the multi-scale study of the inner structure of fault zones.

physics.geo-ph↗

arXiv2006

Lead-lag cross-sectional structure and detection of correlated-anticorrelated regime shifts: Application to the volatilities of inflation and economic growth rates

We have recently introduced the ``thermal optimal path'' (TOP) method to investigate the real-time lead-lag structure between two time series. The TOP method consists in searching for a robust noise-averaged optimal path of the distance matrix along which the two time series have the greatest similarity. Here, we generalize the TOP method by introducing a more general definition of distance which takes into account possible regime shifts between positive and negative correlations. This generalization to track possible changes of correlation signs is able to identify possible transitions from one convention (or consensus) to another. Numerical simulations on synthetic time series verify that the new TOP method performs as expected even in the presence of substantial noise. We then apply it to investigate changes of convention in the dependence structure between the historical volatilities of the USA inflation rate and economic growth rate. Several measures show that the new TOP method significantly outperforms standard cross-correlation methods.

physics.soc-ph↗

arXiv2006

Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling

Song, Havlin and Makse (2005) have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number $N_V$ of boxes of size $\ell$ needed to cover all the nodes of a cellular network was found to scale as the power law $N_V \sim (\ell+1)^{-D_V}$ with a fractal dimension $D_V=3.53\pm0.26$. We propose a new box-counting method based on edge-covering, which outperforms the node-covering approach when applied to strictly self-similar model networks, such as the Sierpinski network. The minimal number $N_E$ of boxes of size $\ell$ in the edge-covering method is obtained with the simulated annealing algorithm. We take into account the possible discrete scale symmetry of networks (artifactual and/or real), which is visualized in terms of log-periodic oscillations in the dependence of the logarithm of $N_E$ as a function of the logarithm of $\ell$. In this way, we are able to remove the bias of the estimator of the fractal dimension, existing for finite networks. With this new methodology, we find that $N_E$ scales with respect to $\ell$ as a power law $N_E \sim \ell^{-D_E}$ with $D_E=2.67\pm0.15$ for the 43 cellular networks previously analyzed by Song, Havlin and Makse (2005). Bootstrap tests suggest that the analyzed cellular networks may have a significant log-periodicity qualifying a discrete hierarchy with a scaling ratio close to 2. In sum, we propose that our method of edge-covering with simulated annealing and log-periodic sampling minimizes the significant bias in the determination of fractal dimensions in log-log regressions.

cond-mat.dis-nn↗

arXiv2005

Is There a Real-Estate Bubble in the US?

We analyze the quarterly average sale prices of new houses sold in the USA as a whole, in the northeast, midwest, south, and west of the USA, in each of the 50 states and the District of Columbia of the USA, to determine whether they have grown faster-than-exponential which we take as the diagnostic of a bubble. We find that 22 states (mostly Northeast and West) exhibit clear-cut signatures of a fast growing bubble. From the analysis of the S&P 500 Home Index, we conclude that the turning point of the bubble will probably occur around mid-2006.

physics.soc-ph↗

arXiv2005

Fundamental Factors versus Herding in the 2000-2005 US Stock Market and Prediction

We present a general methodology to incorporate fundamental economic factors to our previous theory of herding to describe bubbles and antibubbles. We start from the strong form of Rational Expectation and derive the general method to incorporate factors in addition to the log-periodic power law (LPPL) signature of herding developed in ours and others' works. These factors include interest rate, interest spread, historical volatility, implied volatility and exchange rates. Standard statistical AIC and Wilks tests allow us to compare the explanatory power of the different proposed factor models. We find that the historical volatility played the key role before August of 2002. Around October 2002, the interest rate dominated. In the first six months of 2003, the foreign exchange rate became the key factor. Since the end of 2003, all factors have played an increasingly large role. However, the most surprising result is that the best model is the second-order LPPL without any factor. We thus present a scenario for the future evolution of the US stock market based on the extrapolation of the fit of the second-order LPPL formula, which suggests that herding is still the dominating force and that the unraveling of the US stock market antibubble since 2000 is still qualitatively similar to (but quantitatively different from) the Japanese Nikkei case after 1990.

physics.soc-ph↗

arXiv2005

Self-fulfilling Ising Model of Financial Markets

We study a dynamical Ising model of agents' opinions (buy or sell) with coupling coefficients reassessed continuously in time according to how past external news (magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we test within the same model the hypothesis that agents are rational versus irrational. We find that the stylized facts of financial markets are reproduced only when agents are over-confident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point.

physics.soc-ph↗

arXiv2005

Importance of Positive Feedbacks and Over-confidence in a Self-Fulfilling Ising Model of Financial Markets

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are over-confident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

cond-mat.stat-mech↗

arXiv2004

A Mechanism for Pockets of Predictability in Complex Adaptive Systems

We document a mechanism operating in complex adaptive systems leading to dynamical pockets of predictability (``prediction days''), in which agents collectively take predetermined courses of action, transiently decoupled from past history. We demonstrate and test it out-of-sample on synthetic minority and majority games as well as on real financial time series. The surprising large frequency of these prediction days implies a collective organization of agents and of their strategies which condense into transitional herding regimes.

cond-mat.stat-mech↗

arXiv2003

Bath's law Derived from the Gutenberg-Richter law and from Aftershock Properties

The empirical Bath's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we show that the origin of Bath's law is to be found in the selection procedure used to define mainshocks and aftershocks rather than in any difference in the mechanisms controlling the magnitude of the mainshock and of the aftershocks. We use the ETAS model of seismicity, which provides a more realistic model of aftershocks, based on (i) a universal Gutenberg-Richter (GR) law for all earthquakes, and on (ii) the increase of the number of aftershocks with the mainshock magnitude. Using numerical simulations of the ETAS model, we show that this model is in good agreement with Bath's law in a certain range of the model parameters.

physics.geo-ph↗