A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\in \Re)$ ($S_{1} \equiv S_{BG}=-k\sum\limits_{i=1}^{W}p_{i} \ln p_{i}$). More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices $q$ in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation $q_{stat}+q_{sens}=2$ is numerically satisfied, $q_{stat}$ and $q_{sens}$ being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.Comment: Invited paper to appear in special issue of Eur. Phys. J. B dedicated to econophysics, edited by T. Di Matteo and T. Aste. 7 page

Carbon allocation and carbon isotope fluxes in the plant-soil-atmosphere continuum: a review

The terrestrial carbon (C) cycle has received increasing interest over the past few decades, however, there is still a lack of understanding of the fate of newly assimilated C allocated within plants and to the soil, stored within ecosystems and lost to the atmosphere. Stable carbon isotope studies can give novel insights into these issues. In this review we provide an overview of an emerging picture of plant-soil-atmosphere C fluxes, as based on C isotope studies, and identify processes determining related C isotope signatures. The first part of the review focuses on isotopic fractionation processes within plants during and after photosynthesis. The second major part elaborates on plant-internal and plant-rhizosphere C allocation patterns at different time scales (diel, seasonal, interannual), including the speed of C transfer and time lags in the coupling of assimilation and respiration, as well as the magnitude and controls of plant-soil C allocation and respiratory fluxes. Plant responses to changing environmental conditions, the functional relationship between the physiological and phenological status of plants and C transfer, and interactions between C, water and nutrient dynamics are discussed. The role of the C counterflow from the rhizosphere to the aboveground parts of the plants, e.g. via CO<sub>2</sub> dissolved in the xylem water or as xylem-transported sugars, is highlighted. The third part is centered around belowground C turnover, focusing especially on above- and belowground litter inputs, soil organic matter formation and turnover, production and loss of dissolved organic C, soil respiration and CO<sub>2</sub> fixation by soil microbes. Furthermore, plant controls on microbial communities and activity via exudates and litter production as well as microbial community effects on C mineralization are reviewed. A further part of the paper is dedicated to physical interactions between soil CO<sub>2</sub> and the soil matrix, such as CO<sub>2</sub> diffusion and dissolution processes within the soil profile. Finally, we highlight state-of-the-art stable isotope methodologies and their latest developments. From the presented evidence we conclude that there exists a tight coupling of physical, chemical and biological processes involved in C cycling and C isotope fluxes in the plant-soil-atmosphere system. Generally, research using information from C isotopes allows an integrated view of the different processes involved. However, complex interactions among the range of processes complicate or currently impede the interpretation of isotopic signals in CO<sub>2</sub> or organic compounds at the plant and ecosystem level. This review tries to identify present knowledge gaps in correctly interpreting carbon stable isotope signals in the plant-soil-atmosphere system and how future research approaches could contribute to closing these gaps

The dynamics of financial stability in complex networks

We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange `economic energy', forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability

Turbulent luminance in impassioned van Gogh paintings

We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation

Persistence Probabilities of the German DAX and Shanghai Index

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical simulations of some microscopic models are also performed. Around the fixed point $z_0=0$, the interacting herding model produces the scaling behavior of the real markets

How to quantify deterministic and random influences on the statistics of the foreign exchange market

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can be estimated. Finally, we present an explicite Fokker-Planck equation which models very precisely the empirical probabilitiy distributions.Comment: 3 figure

Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization

The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified ways of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems, and for information service providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or

Multifractality in Time Series

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000

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