Statistical pairwise interaction model of stock market

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.Comment: 11 pages, 8 figure

The Fractal Geometry of the Cosmic Web and its Formation

The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. A non-lacunar multifractal geometry can encompass three fundamental descriptions of the cosmic structure, namely, the web structure, hierarchical clustering, and halo distributions. Furthermore, it explains our present knowledge of cosmic voids. In this way, a unified theory of the large-scale structure of the universe seems to emerge. The multifractal spectrum that we obtain significantly differs from the one of the adhesion model and conforms better to the laws of gravity. The formation of the cosmic web is best modeled as a type of turbulent dynamics, generalizing the known methods of Burgers turbulence.Comment: 35 pages, 8 figures; corrected typos, added references; further discussion of cosmic voids; accepted by Advances in Astronom

Estimating the historical and future probabilities of large terrorist events

Quantities with right-skewed distributions are ubiquitous in complex social systems, including political conflict, economics and social networks, and these systems sometimes produce extremely large events. For instance, the 9/11 terrorist events produced nearly 3000 fatalities, nearly six times more than the next largest event. But, was this enormous loss of life statistically unlikely given modern terrorism's historical record? Accurately estimating the probability of such an event is complicated by the large fluctuations in the empirical distribution's upper tail. We present a generic statistical algorithm for making such estimates, which combines semi-parametric models of tail behavior and a nonparametric bootstrap. Applied to a global database of terrorist events, we estimate the worldwide historical probability of observing at least one 9/11-sized or larger event since 1968 to be 11-35%. These results are robust to conditioning on global variations in economic development, domestic versus international events, the type of weapon used and a truncated history that stops at 1998. We then use this procedure to make a data-driven statistical forecast of at least one similar event over the next decade.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS614 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org