Criticality and finite size effects in a simple realistic model of stock market

We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple argument, we show that, in Minority Games, the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets as critical systems.Comment: 4 pages, 4 figure

Volatility clustering and scaling for financial time series due to attractor bubbling

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or

Scaling of the distribution of price fluctuations of individual companies

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 US companies for the 2-year period 1994--95, and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-year period 1962--96. We study the probability distribution of returns over varying time scales $\Delta t$, where $\Delta t$ varies by a factor of $\approx 10^5$---from 5 min up to $\approx$ 4 years. For time scales from 5~min up to approximately 16~days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent $\alpha \approx 3$ ---well outside the stable L\'evy regime $0 < \alpha < 2$. For time scales $\Delta t \gg (\Delta t)_{\times} \approx 16$days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.Comment: 10pages 2 column format with 11 eps figures. LaTeX file requiring epsf, multicol,revtex. Submitted to PR

Universal and non-universal properties of cross-correlations in financial time series

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum--a situation reminiscent of results in localization theory.Comment: 14 pages, 3 figures, Revte

Size Effects in Agent-Based Macroeconomic Models: An Initial Investigation

We investigate the scale-free property of an agent-based macroeconomic model initially proposed by Wright (2005), called the Social Architecture (SA) model. The SA model has been shown to be able to replicate a number of important features of a macroeconomy, such as patterns concerning economic growth, business cycles, industrial dynamics and income distribution. We explore whether macroeconomic stylized features resulting from this model are robust when the number of agents populating the (model) economy vary. We simulate the model by systematically varying the agent population with 100, 500, 1000, 2,000, 4,000, 8,000 and 10,000 agents. Our results indicate that the SA model does exhibit significant size effects for several important variables

Architecture and Gender : Lessons from Building Archaeology in Africa

Peer reviewe

Glacial history affected phenotypic differentiation in the Alpine plant Campanula thyrsoides

Numerous widespread Alpine plant species show molecular differentiation among populations from distinct regions. This has been explained as the result of genetic drift during glacial survival in isolated refugia along the border of the European Alps. Since genetic drift may affect molecular markers and phenotypic traits alike, we asked whether phenotypic differentiation mirrors molecular patterns among Alpine plant populations from different regions. Phenotypic traits can be under selection, so we additionally investigated whether part of the phenotypic differentiation can be explained by past selection and/or current adaptation. Using the monocarpic Campanula thyrsoides as our study species, a common garden experiment with plants from 21 populations from four phylogeographic groups located in regions across the Alps and the Jura Mountains was performed to test for differentiation in morphological and phenological traits. Past selection was investigated by comparing phenotypic differentiation among and within regions with molecular differentiation among and within regions. The common garden results indicated regional differentiation among populations for all investigated phenotypic traits, particularly in phenology. Delayed flowering in plants from the South-eastern Alps suggested adaptation to long sub-mediterranean summers and contrasted with earlier flowering of plants experiencing shorter growing seasons in regions with higher elevation to the West. Comparisons between molecular and phenotypic differentiation revealed diversifying selection among regions in height and biomass, which is consistent with adaptation to environmental conditions in glacial refugia. Within regions, past selection acted against strong diversification for most phenotypic traits, causing restricted postglacial adaptation. Evidence consistent with post-glacial adaptation was also given by negative correlation coefficients between several phenotypic traits and elevation of the population's origin. In conclusion, our study suggests that, irrespective of adaptation of plants to their current environment, glacial history can have a strong and long-lasting influence on the phenotypic evolution of Alpine plants

Differentiation in morphology and flowering phenology between two Campanula thyrsoides L. subspecies

Subspecies are usually characterized by sets of morphological discontinuities. By means of common garden experiments, we investigated genetic differentiation in morphological and phenological traits in two geographically disjunct subspecies of Campanula thyrsoides L., i.e. subsp. thyrsoides (= C.* thyrsoides) occurring in the European Alps and Jura Mountains, and subsp. carniolica (= C.* carniolica) occurring in the Southeastern Alps and the Dinaric Arc. Nine out of 16 investigated traits were significantly different between C.* thyrsoides and C.* carniolica. For C.* carniolica inflorescence length was 1.4×, and above-ground biomass 2.7× higher, while flower density was significantly lower. Campanula* carniolica also showed delayed flowering and flower development from bottom to top compared to C.* thyrsoides which flowered from top to bottom. The inflorescence growth was indeterminate and flowering took several weeks in C.* carniolica, whereas C.* thyrsoides showed determinate flowering, rapidly opening all flowers within a few days. This differentiation in flowering phenology is likely to be adaptive. The submediterranean climate favours indeterminate flowering in C.* carniolica, allowing ongoing growth of the inflorescence throughout the long summer until environmental conditions worsen, whereas determinate and early flowering in C.* thyrsoides is favourable in the short growing season in the high Alps where seed production must be secured before temperature drops. Glacial survival in refugia with different climates (alpine vs. submediterranean) may have caused this regional differentiation