Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfvén Brésillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high MHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation.     

Cascades and self-organized criticality

We generalize the model of self-organized critical systems to cases where due to some internal degrees of freedom the local conservation law is violated. This can be realized by taking a transfer ratio different from the critical one in a sand pile model (global violation) or allowing fluctuations around the critical ratio (local violation). In the first case the deviation from the critical ratioR is a critical parameter and the characteristic avalanche size diverges as |R|^– . In the second case the global conservation assures criticality; however, our numerical results indicate that the model is in a new universality class.On leave from Institute for Experimental Physics, JATE University, Dóm tèr 9, Szeged, H-6720 Hungary.On leave from Institute for Technical Physics, H-1325 Budapest, Hungary.     

Market mill dependence pattern in the stock market: Multiscale conditional dynamics

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry-generating component of the conditional probability distribution result in the “elementary” market mill pattern. This asymmetry-generating component matches the empirical distribution obtained from the market data. Multiple time scale considerations make the resulting “composite” mill similar to the empirical market mill patterns. Multiscale model also reflects a multi-agent nature of the market. Interpretation of variations of asymmetry patterns of individual stocks in terms of specific deformations of the fundamental market mill asymmetry patterns is described.     

An agent-based model of stock markets incorporating momentum investors

It has been widely accepted that there exist investors who adopt momentum strategies in real stock markets. Understanding the momentum behavior is of both academic and practical importance. For this purpose, we propose and study a simple agent-based model of trading incorporating momentum investors and random investors. The random investors trade randomly all the time. The momentum investors could be idle, buying or selling, and they decide on their action by implementing an action threshold that assesses the most recent price movement. The model is able to reproduce some of the stylized facts observed in real markets, including the fat-tails in returns, weak long-term correlation and scaling behavior in the kurtosis of returns. An analytic treatment of the model relates the model parameters to several quantities that can be extracted from real data sets. To illustrate how the model can be applied, we show that real market data can be used to constrain the model parameters, which in turn provide information on the behavior of momentum investors in different markets.     

Intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market

This study provides empirical evidence of the relationship between spot and futures markets in Korea. In particular, the study focuses on the volatility spillover relationship between spot and futures markets by using three high-frequency (10 min, 30 min, and 1 h time-scales) intraday data sets of KOSPI 200 spot and futures contracts. The results indicate a strong bi-directional causal relationship between futures and spot markets, suggesting that return volatility in the spot market can influence that in the futures market and vice versa. Thus, the results indicate that new information is reflected in futures and spot markets simultaneously. This bi-directional causal relationship provides market participants with important guidance on understanding the intraday information transmission between the two markets. Thus, on a given trading day, there may be sudden and sharp increases or decreases in return volatility in the Korean stock market as a result of positive feedback and synchronization of spot and futures markets.     

A finite-dimensional quantum model for the stock market

We present a finite-dimensional version of the quantum model for the stock market proposed in C. Zhang and L. Huang [A quantum model for the stock market, Physica A 389 (2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite-dimensional Hilbert space. The rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems, and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite Fourier transform. The stock return in equilibrium is described by a finite Gaussian function, and the time evolution of the stock price, directly related to the rate of return, is obtained by numerically solving a Schrödinger type equation.     

Modeling interactions of trading volumes in financial dynamics

A dynamic herding model with interactions of trading volumes is introduced. At time t, an agent trades with a probability, which depends on the ratio of the total trading volume at time t−1 to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model can reproduce the power-law distributions of the trading volume, number of trades and price return, and the probable relation between them. The exponents are tunable by adjusting the values of the parameters, but show slight deviation from those revealed in empirical studies. Moreover, the time series generated are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.     

A postcard from the past: The behavior of U.S. stock markets during 1871-1938

In this article, we study the behavior of the stock prices of a subset of eight U.S. industries from the late 1800's to the Great Depression. In particular, we focus on the potential presence of volatility shifts, the persistence of volatility, and on the degree of co-movement of stock returns prior to and during the Great Depression. Our findings show that stock markets became particularly volatile toward the mid 1930's, but that the persistence of volatility tended to decrease around the same time period. In that regard, we find little evidence that such behavior is driven by trading volume. In addition, we conclude that the overall correlation across the different industries was relatively more significant in statistical terms from 1921 to part of the Great Depression (1929-1931; 1933-1934 and 1936).     

Attaining and maintaining criticality in a neuronal network model

We propose a cellular automaton model for neuronal networks that combines short-term synaptic plasticity with long-term metaplasticity. We investigate how these two mechanisms contribute to attaining and maintaining operation at the critical point. We find that short-term plasticity, represented in the model by synaptic depression and synaptic recovery, is sufficient to allow the system to attain the critical state, if the level of plasticity is properly chosen. However, it is not sufficient to maintain the criticality if the system is perturbed. But the long time scale change in the short-term plasticity, a change in the way synaptic efficacy is modified, allows the system to recover from perturbation. Working together, these two time scales of plasticity could help the system to attain and maintain criticality, leading to a self-organized critical state.     

Correlation and volatility in an Indian stock market: A random matrix approach

We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index.     

Topological properties of stock market networks: The case of Brazil

This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network.     

Agreement dynamics of finite-memory language games on networks

We propose a Finite-Memory Naming Game (FMNG) model with respect to the bounded rationality of agents or finite resources for information storage in communication systems. We study its dynamics on several kinds of complex networks, including random networks, small-world networks and scale-free networks. We focus on the dynamics of the FMNG affected by the memory restriction as well as the topological properties of the networks. Interestingly, we found that the most important quantity, the convergence time of reaching the consensus, shows some non-monotonic behaviors by varying the average degrees of the networks with the existence of the fastest convergence at some specific average degrees. We also investigate other main quantities, such as the success rate in negotiation, the total number of words in the system and the correlations between agents of full memory and the total number of words, which clearly explain the nontrivial behaviors of the convergence. We provide some analytical results which help better understand the dynamics of the FMNG. We finally report a robust scaling property of the convergence time, which is regardless of the network structure and the memory restriction.     

The minimal length uncertainty and the quantum model for the stock market

We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the fourth power of the trend. We study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system. The connection between the information frequency and the transition probabilities is discussed finally.     

Stock market dynamics: Before and after stock market crashes

This paper presents a brief analysis on the distribution of magnitude of major stock market shocks. Based on the Gutenberg-Richter law in geophysics, we model the dynamics of market index returns prior and after major crashes in search of statistical regularities. For a large number of market crashes, our analysis suggests that the distribution of market volatility before and after the stock market crash is described well by the Gutenberg-Richter law, which reflects the scale-invariance and self-similarity of the underlying dynamics by a robust power-law relation. In addition, the rate of the decay of the aftershock sequence is well described by another power law, which is known as the Omori law. Power law relaxation seems to be a common behavior observed in complex systems such as the financial markets.     

Probability distribution function and multiscaling properties in the Korean stock market

We consider the probability distribution function (pdf) and the multiscaling properties of the index and the traded volume in the Korean stock market. We observed the power law of the pdf at the fat tail region for the return, volatility, the traded volume, and changes of the traded volume. We also investigate the multifractality in the Korean stock market. We consider the multifractality by the detrended fluctuation analysis (MFDFA). We observed the multiscaling behaviors for index, return, traded volume, and the changes of the traded volume. We apply MFDFA method for the randomly shuffled time series to observe the effects of the autocorrelations. The multifractality is strongly originated from the long time correlations of the time series.     

Evolutionary model on market ecology of investors and investments

The interactions between investors and investments are of significant importance to understand the dynamics of financial markets. An evolutionary model is proposed to investigate the dynamic behaviors of investors and investments in a market ecology. The investors are divided into two groups, active ones and passive ones, distinguished by different selection capabilities based on the partial information, while the investments are simply categorized as good ones and bad ones. Without external influence, the system consisting of both investors and investments can self-organize to a quasi-stationary state according to their own strategies associating with the gains of market information. The model suggests that the partial information asymmetry of investors and various qualities of investments commonly give rise to a diverse dynamic behavior of the system by quantifying the fraction of active investors and of good investment at the quasi-stationary state.     

Complexity and criticality in fusion, space and astrophysical plasmas

Techniques from complexity and criticality theory have fruitful applications to a wide range of natural and laboratory plasma systems. Here we review examples that have direct observational relevance, spanning fusion, the Earth's magnetosphere, the sun and astrophysical accretion disks. The complex systems techniques range from sandpiles to a novel loop-based dynamical model, together with modern approaches to model-independent data analysis.     

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

We tested 45 indices and common stocks in the South African stock market for the possible existence of a bubble over the period from January 2003 to May 2006. A bubble is defined by a faster-than-exponential acceleration with significant log-periodic oscillations. These two traits are analyzed using different methods. Sensitivity tests show that the estimated parameters are robust. With the insight of 6 additional months of data since the analysis was performed, we observe that many of the stocks on the South African market experienced an abrupt drop at 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 time in 2007, similarly to what happened in the US market from October 1997 to August 1998.