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Recent research has focused on understanding how cooperation is fostered through various mechanisms in cognitive settings, particularly through pairwise interactions. However, real-world interactions often extend beyond simple dyads, including multiple cliques with both pairwise and higher-order interactions. These complex interactions influence how individuals perceive and adapt their strategies based on social norms. We here introduce a model that explores the evolution of collective strategies and social norms within a heterogeneous environment, encompassing both dyadic and three-body interactions. We find that social norms play a crucial role in promoting cooperation in comparison to simply imitating the most successful neighbor. We also show that the rise of prosocial norms leads to increased cooperation across various social dilemmas, often resulting in shifts from defective to cooperative behavior. Additionally, we observe that a moderate level of information privacy helps sustaining prosocial norms and curtails antisocial tendencies, even in situations where mutual defection might seem advantageous. Our research thus offers insights into the evolution of cooperation through the lens of social norm diffusion in higher-order networks., Comment: 12 pages, 9 figures

Using a unique data set containing about 15.06 million truck transportation records in five months, we investigate the highway freight transportation diversity of 338 Chinese cities based on the truck transportation probability $p_{ij}$ from one city to the other. The transportation probabilities are calculated from the radiation model based on the geographic distance and its cost-based version based on the driving distance as the proxy of cost. For each model, we consider both the population and the gross domestic product, and find quantitatively very similar results. We find that the transportation probabilities have nice power-law tails with the tail exponents close to 0.5 for all the models. The two transportation probabilities in each model fall around the diagonal $p_{ij}=p_{ji}$ but are often not the same. In addition, the corresponding transportation probabilities calculated from the raw radiation model and the cost-based radiation model also fluctuate around the diagonal $p_{ij}^{\rm{geo}}=p_{ij}^{\rm{cost}}$. We calculate four sets of highway truck transportation diversity according to the four sets of transportation probabilities that are found to be close to each other for each city pair. Further, it is found that the population, the gross domestic product, the in-flux, and the out-flux scale as power laws with respect to the transportation diversity in the raw and cost-based radiation models. It implies that a more developed city usually has higher diversity in highway truck transportation, which reflects the fact that a more developed city usually has a more diverse economic structure., Comment: 8 pages including 5 figures and 1 table

Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these extremes. We find that the waiting time between consecutive extremes (recurrence interval) follow a $q$-exponential distribution and the sizes of extremes above the thresholds (exceeding size) conform to a generalized Pareto distribution. We also find that there is a significant correlation between recurrence intervals and exceeding sizes. We thus model the joint distribution of recurrence intervals and exceeding sizes through connecting the two corresponding marginal distributions with the Frank and AMH copula functions, and apply this joint distribution to estimate the hazard probability to observe another extreme in $\Delta t$ time since the last extreme happened $t$ time ago. Furthermore, an extreme predicting model based on RIA-EVT-Copula is proposed by applying a decision-making algorithm on the hazard probability. Both in-sample and out-of-sample tests reveal that this new extreme forecasting framework has better performance in prediction comparing with the forecasting model based on the hazard probability only estimated from the distribution of recurrence intervals. Our results not only shed a new light on understanding the occurring pattern of extremes in financial markets, but also improve the accuracy to predict financial extremes for risk management., Comment: 14 pages, 5 figures, and 4 tables

Uncovering the risk transmitting path within economic sectors in China is crucial for understanding the stability of the Chinese economic system, especially under the current situation of the China-US trade conflicts. In this paper, we try to uncover the risk spreading channels by means of volatility spillovers within the Chinese sectors using stock market data. By applying the generalized variance decomposition framework based on the VAR model and the rolling window approach, a set of connectedness matrices is obtained to reveal the overall and dynamic spillovers within sectors. It is found that 17 sectors (mechanical equipment, electrical equipment, utilities, and so on) are risk transmitters and 11 sectors (national defence, bank, non-bank finance, and so on) are risk takers during the whole period. During the periods with the extreme risk events (the global financial crisis, the Chinese interbank liquidity crisis, the Chinese stock market plunge, and the China-US trade war), we observe that the connectedness measures significantly increase and the financial sectors play a buffer role in stabilizing the economic system. The robust tests suggest that our results are not sensitive to the changes of model parameters. Our results not only uncover the spillover effects within the Chinese sectors, but also highlight the deep understanding of the risk contagion patterns in the Chinese stock markets., Comment: 17 pages, 7 figures, and 3 tables

Empirical investor networks (EIN) proposed by \cite{Ozsoylev-Walden-Yavuz-Bildik-2014-RFS} are assumed to capture the information spreading path among investors. Here, we perform a comparative analysis between the EIN and the cellphone communication networks (CN) to test whether EIN is an information exchanging network from the perspective of the layer structures of ego networks. We employ two clustering algorithms ($k$-means algorithm and $H/T$ break algorithm) to detect the layer structures for each node in both networks. We find that the nodes in both networks can be clustered into two groups, one that has a layer structure similar to the theoretical Dunbar Circle corresponding to that the alters in ego networks exhibit a four-layer hierarchical structure with the cumulative number of 5, 15, 50 and 150 from the inner layer to the outer layer, and the other one having an additional inner layer with about 2 alters compared with the Dunbar Circle. We also find that the scale ratios, which are estimated based on the unique parameters in the theoretical model of layer structures \citep{Tamarit-Cuesta-Dunbar-Sanchez-2018-PNAS}, conform to a log-normal distribution for both networks. Our results not only deepen our understanding on the topological structures of EIN, but also provide empirical evidence of the channels of information diffusion among investors., Comment: 9 pages, 9 figues, 3 tables

User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to human's circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity $\Delta\alpha$ is negatively correlated with the maximum activity ($p$-value=0.070) and the time to the maximum activity ($p$-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations., Comment: 9 pages including 8 figures

Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are numerically and analytically investigated for certain time series. We derive the degree distributions of HVGs through an iterative construction process of HVGs. The degree distributions of the HVG and the directed HVG for random series are derived to be exponential, which confirms the analytical results from other methods. We also obtained the analytical expressions of degree distributions of HVGs and in-degree and out-degree distributions of directed HVGs transformed from multifractal binomial measures, which agree excellently with numerical simulations., Comment: 7 pages, 4 figures

By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock Exchange Composite Index (SZCI). The characteristics of the corresponding multifractal spectra are defined as a measurement of market volatility. It is found that there is a statistically significant relationship between the stock index returns and the spectral characteristics, which can be applied to forecast the future market return. The in-sample and out-of-sample tests on the return predictability of multifractal characteristics indicate the spectral width $\Delta {\alpha}$ is a significant and positive excess return predictor. Our results shed new lights on the application of multifractal nature in asset pricing., Comment: 2 figures, 5 tables, and 12 pages

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis., Comment: A review paper contains 145 pages

In this paper, we investigate the cooling-off effect (opposite to the magnet effect) from two aspects. Firstly, from the viewpoint of dynamics, we study the existence of the cooling-off effect by following the dynamical evolution of some financial variables over a period of time before the stock price hits its limit. Secondly, from the probability perspective, we investigate, with the logit model, the existence of the cooling-off effect through analyzing the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 and inspecting the trading period from the opening phase prior to the moment that the stock price hits its limits. A comparison is made of the properties between up-limit hits and down-limit hits, and the possible difference will also be compared between bullish and bearish market state by dividing the whole period into three alternating bullish periods and three bearish periods. We find that the cooling-off effect emerges for both up-limit hits and down-limit hits, and the cooling-off effect of the down-limit hits is stronger than that of the up-limit hits. The difference of the cooling-off effect between bullish period and bearish period is quite modest. Moreover, we examine the sub-optimal orders effect, and infer that the professional individual investors and institutional investors play a positive role in the cooling-off effects. All these findings indicate that the price limit trading rule exerts a positive effect on maintaining the stability of the Chinese stock markets.

The availability of big data recorded from massively multiplayer online role-playing games (MMORPGs) allows us to gain a deeper understanding of the potential connection between individuals' network positions and their economic outputs. We use a statistical filtering method to construct dependence networks from weighted friendship networks of individuals. We investigate the 30 distinct motif positions in the 13 directed triadic motifs which represent microscopic dependences among individuals. Based on the structural similarity of motif positions, we further classify individuals into different groups. The node position diversity of individuals is found to be positively correlated with their economic outputs. We also find that the economic outputs of leaf nodes are significantly lower than that of the other nodes in the same motif. Our findings shed light on understanding the influence of network structure on economic activities and outputs in socioeconomic system., Comment: 19 pages, 5 figures

Based on the order flow data of a stock and its warrant, the immediate price impacts of market orders are estimated by two competitive models, the power-law model (PL model) and the logarithmic model (LG model). We find that the PL model is overwhelmingly superior to the LG model, regarding the robustness of the estimated parameters and the accuracy of out-of-sample forecasting. We also find that the price impacts of ask and bid orders are consistent with each other for filled trades, since significant positive correlations are observed between the model parameters of both types of orders. Our findings may provide valuable insights for optimal trade execution., Comment: 11 Latex pages including 4 figures and 4 tables. accepted by International Journal of Modern Physics B

China's stock market is the largest emerging market all over the world. It is widely accepted that the Chinese stock market is far from efficiency and it possesses possible linear and nonlinear dependence. We study the predictability of returns in the Chinese stock market by employing the wild bootstrap automatic variance ratio test and the generalized spectral test. We find that the return predictability vary over time and significant return predictability is observed around market turmoils. Our findings are consistent with the Adaptive Markets Hypothesis and have practical implications for market participants., Comment: 11 Latex pages including 2 figures and 1 table

Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable to detect the cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to the pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and find an intriguing joint multifractal behavior., Comment: 11 pages and 5 figures. arXiv admin note: text overlap with arXiv:1610.09519

Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross correlations based on wavelet analysis, termed multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, the empirical joint multifractality of MFXWT is found to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indexes and uncover intriguing joint multifractal nature in pairs of index returns and volatilities.

Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are predictable on the short term. Examining a range of different types of returns and thresholds we find that recurrence intervals follow a $q$-exponential distribution, which we then use to theoretically derive the hazard probability $W(\Delta t |t)$. Maximizing the usefulness of extreme forecasts to define an optimized hazard threshold, we indicates a financial extreme occurring within the next day when the hazard probability is greater than the optimized threshold. Both in-sample tests and out-of-sample predictions indicate that these forecasts are more accurate than a benchmark that ignores the predictive signals. This recurrence interval finding deepens our understanding of reoccurring extreme returns and can be applied to forecast extremes in risk management., Comment: 18 pages, 5 figues, 3 tables

People in modern societies form different social networks through numerous means of communication. These communication networks reflect different aspects of human's societal structure. The billing records of calls among mobile phone users enable us to construct a directed calling network (DCN) and its Bonferroni network (SVDCN) in which the preferential communications are statistically validated. Here we perform a comparative investigation of the cliques of the original DCN and its SVDCN constructed from the calling records of more than nine million individuals in Shanghai over a period of 110 days. We find that the statistical properties of the cliques of the two calling networks are qualitatively similar and the clique members in the DCN and the SVDCN exhibit idiosyncratic behaviors quantitatively. Members in large cliques are found to be spatially close to each other. Based on the clique degree profile of each mobile phone user, the most active users in the two calling networks can be classified in to several groups. The users in different groups are found to have different calling behaviors. Our study unveils interesting communication behaviors among mobile phone users that are densely connected to each other., Comment: 18 pages, 10 figures

Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities., Comment: 19 pages, 5 figures

Humans are heterogenous and the behaviors of individuals could be different from that at the population level. We conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73'339 anonymous cellphone users with the same truncated Weibull distribution of inter-call durations. We find that the individual call events exhibit a pattern of bursts, in which high activity periods are alternated with low activity periods. Surprisingly, the number of events in high activity periods are found to conform to a power-law distribution at the population level, but follow an exponential distribution at the individual level, which is a hallmark of absence of memory in individual call activities. Such exponential distribution is also observed for the number of events in low activity periods. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain giving very good agreement with the empirical distributions using the parameters estimated from real data for about half of the individuals in our sample. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we explain the difference with previous population level studies, purporting the existence of power-law distributions, via the "Superposition of Distributions" mechanism: The superposition of many exponential distributions of activities with a power-law distribution of their characteristic scales leads to a power-law distribution of the activities at the population level., Comment: 16 pages, 7 figures

Being able to forcast extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between volatilities exceeding a certain threshold $Q$ for a fixed expected recurrence time $\tau_Q$. We find that the recurrence intervals are well approximated by the $q$-exponential distribution for all stocks and all $\tau_Q$ values. Thus a analytical formula for determining the hazard probability $W(\Delta t |t)$ that a volatility above $Q$ will occur within a short interval $\Delta t$ if the last volatility exceeding $Q$ happened $t$ periods ago can be directly derived from the $q$-exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above $Q$ based on the hazard probability. Using a "receiver operator characteristic" (ROC) analysis, we find that this predicting method efficiently forecasts the occurrance of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and more accurately quantify financial risks in stock markets., Comment: 13 pages and 7 figures

This paper reexamines the profitability of loser, winner and contrarian portfolios in the Chinese stock market using monthly data of all stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange covering the period from January 1997 to December 2012. We find evidence of short-term and long-term contrarian profitability in the whole sample period when the estimation and holding horizons are 1 month or longer than 12 months and the annualized returns of contrarian portfolios increases with the estimation and holding horizons. We perform subperiod analysis and find that the long-term contrarian effect is significant in both bullish and bearish states while the short-term contrarian effect disappears in bullish states. We compare the performance of contrarian portfolios based on different grouping manners in the estimation period and unveil that decile grouping outperforms quintile grouping and tertile grouping, which is more evident and robust in the long run. Generally, loser portfolios and winner portfolios have positive returns and loser portfolios perform much better than winner portfolios. Both loser and winner portfolios in bullish states perform better than those in the whole sample period. In contrast, loser and winner portfolios have smaller returns in bearish states in which loser portfolio returns are significant only in the long term and winner portfolio returns become insignificant. These results are robust to the one-month skipping between the estimation and holding periods and for the two stock exchanges. Our findings show that the Chinese stock market is not efficient in the weak form. These findings also have obvious practical implications for financial practitioners., Comment: 24 pages (including 4 figures and 9 tables) + 5 supplementary figures + 10 supplementary tables

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. Many long-term correlated time series in real systems contain various trends. We investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trend, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends., Comment: 13 Latex pages including 3 figures

Technical trading rules have a long history of being used by practitioners in financial markets. Their profitable ability and efficiency of technical trading rules are yet controversial. In this paper, we test the performance of more than seven thousands traditional technical trading rules on the Shanghai Securities Composite Index (SSCI) from May 21, 1992 through June 30, 2013 and Shanghai Shenzhen 300 Index (SHSZ 300) from April 8, 2005 through June 30, 2013 to check whether an effective trading strategy could be found by using the performance measurements based on the return and Sharpe ratio. To correct for the influence of the data-snooping effect, we adopt the Superior Predictive Ability test to evaluate if there exists a trading rule that can significantly outperform the benchmark. The result shows that for SSCI, technical trading rules offer significant profitability, while for SHSZ 300, this ability is lost. We further partition the SSCI into two sub-series and find that the efficiency of technical trading in sub-series, which have exactly the same spanning period as that of SHSZ 300, is severely weakened. By testing the trading rules on both indexes with a five-year moving window, we find that the financial bubble from 2005 to 2007 greatly improve the effectiveness of technical trading rules. This is consistent with the predictive ability of technical trading rules which appears when the market is less efficient., Comment: 11 Latex pages including 2 figures and two tables

Although technical trading rules have been widely used by practitioners in financial markets, their profitability still remains controversial. We here investigate the profitability of moving average (MA) and trading range break (TRB) rules by using the Shanghai Stock Exchange Composite Index (SHCI) from May 21, 1992 through December 31, 2013 and Shenzhen Stock Exchange Composite Index (SZCI) from April 3, 1991 through December 31, 2013. The $t$-test is adopted to check whether the mean returns which are conditioned on the trading signals are significantly different from unconditioned returns and whether the mean returns conditioned on the buy signals are significantly different from the mean returns conditioned on the sell signals. We find that TRB rules outperform MA rules and short-term variable moving average (VMA) rules outperform long-term VMA rules. By applying White's Reality Check test and accounting for the data snooping effects, we find that the best trading rule outperforms the buy-and-hold strategy when transaction costs are not taken into consideration. Once transaction costs are included, trading profits will be eliminated completely. Our analysis suggests that simple trading rules like MA and TRB cannot beat the standard buy-and-hold strategy for the Chinese stock exchange indexes., Comment: 12 pages including 1 figure and 4 tables

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross-correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multi-scale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross-correlation between crude oil and gold futures by taking into consideration the impact of the US dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the MF-DCCA method fails., Comment: 7 Latex pages including 3 figures

Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 to investigate the statistical properties of price limit hits and the dynamical evolution of several important financial variables before stock price hits its limits. We compare the properties of up-limit hits and down-limit hits. We also divide the whole period into three bullish periods and three bearish periods to unveil possible differences during bullish and bearish market states. To uncover the impacts of stock capitalization on price limit hits, we partition all stocks into six portfolios according to their capitalizations on different trading days. We find that the price limit trading rule has a cooling-off effect (object to the magnet effect), indicating that the rule takes effect in the Chinese stock markets. We find that price continuation is much more likely to occur than price reversal on the next trading day after a limit-hitting day, especially for down-limit hits, which has potential practical values for market practitioners., Comment: 18 pages including 8 figures and 2 tables

Constituents of complex systems interact with each other and self-organize to form complex networks. Empirical results show that the link formation process of many real networks follows either the global principle of popularity or the local principle of similarity or a tradeoff between the two. In particular, it has been shown that in social networks individuals exhibit significant homophily when choosing their collaborators. We demonstrate, however, that in populations in which there is a division of labor, skill complementarity is an important factor in the formation of socioeconomic networks and an individual's choice of collaborators is strongly affected by heterophily. We analyze 124 evolving virtual worlds of a popular "massively multiplayer online role-playing game" (MMORPG) in which people belong to three different professions and are allowed to work and interact with each other in a somewhat realistic manner. We find evidence of heterophily in the formation of collaboration networks, where people prefer to forge social ties with people who have professions different from their own. We then construct an economic model to quantify the heterophily by assuming that individuals in socioeconomic systems choose collaborators that are of maximum utility. The results of model calibration confirm the presence of heterophily. Both empirical analysis and model calibration show that the heterophilous feature is persistent along the evolution of virtual worlds. We also find that the degree of complementarity in virtual societies is positively correlated with their economic output. Our work sheds new light on the scientific research utility of virtual worlds for studying human behaviors in complex socioeconomic systems., Comment: 14 Latex pages + 3 figures

This article investigates the correlation structure of the global crude oil market using the daily returns of 71 oil price time series across the world from 1992 to 2012. We identify from the correlation matrix six clusters of time series exhibiting evident geographical traits, which supports Weiner's (1991) regionalization hypothesis of the global oil market. We find that intra-cluster pairs of time series are highly correlated while inter-cluster pairs have relatively low correlations. Principal component analysis shows that most eigenvalues of the correlation matrix locate outside the prediction of the random matrix theory and these deviating eigenvalues and their corresponding eigenvectors contain rich economic information. Specifically, the largest eigenvalue reflects a collective effect of the global market, other four largest eigenvalues possess a partitioning function to distinguish the six clusters, and the smallest eigenvalues highlight the pairs of time series with the largest correlation coefficients. We construct an index of the global oil market based on the eigenfortfolio of the largest eigenvalue, which evolves similarly as the average price time series and has better performance than the benchmark $1/N$ portfolio under the buy-and-hold strategy., Comment: 13 Latex pages including 7 figures and 1 table

In friendship networks, individuals have different numbers of friends, and the closeness or intimacy between an individual and her friends is heterogeneous. Using a statistical filtering method to identify relationships about who depends on whom, we construct dependence networks (which are directed) from weighted friendship networks of avatars in more than two hundred virtual societies of a massively multiplayer online role-playing game (MMORPG). We investigate the evolution of triadic motifs in dependence networks. Several metrics show that the virtual societies evolved through a transient stage in the first two to three weeks and reached a relatively stable stage. We find that the unidirectional loop motif (${\rm{M}}_9$) is underrepresented and does not appear, open motifs are also underrepresented, while other close motifs are overrepresented. We also find that, for most motifs, the overall level difference of the three avatars in the same motif is significantly lower than average, whereas the sum of ranks is only slightly larger than average. Our findings show that avatars' social status plays an important role in the formation of triadic motifs., Comment: 8 Latex pages + 5 figures

Social and economic systems are complex adaptive systems, in which heterogenous agents interact and evolve in a self-organized manner, and macroscopic laws emerge from microscopic properties. To understand the behaviors of complex systems, computational experiments based on physical and mathematical models provide a useful tools. Here, we perform computational experiments using a phenomenological order-driven model called the modified Mike-Farmer (MMF) to predict the impacts of order flows on the autocorrelations in ultra-high-frequency returns, quantified by Hurst index $H_r$. Three possible determinants embedded in the MMF model are investigated, including the Hurst index $H_s$ of order directions, the Hurst index $H_x$ and the power-law tail index $\alpha_x$ of the relative prices of placed orders. The computational experiments predict that $H_r$ is negatively correlated with $\alpha_x$ and $H_x$ and positively correlated with $H_s$. In addition, the values of $\alpha_x$ and $H_x$ have negligible impacts on $H_r$, whereas $H_s$ exhibits a dominating impact on $H_r$. The predictions of the MMF model on the dependence of $H_r$ upon $H_s$ and $H_x$ are verified by the empirical results obtained from the order flow data of 43 Chinese stocks.

Big data open up unprecedented opportunities to investigate complex systems including the society. In particular, communication data serve as major sources for computational social sciences but they have to be cleaned and filtered as they may contain spurious information due to recording errors as well as interactions, like commercial and marketing activities, not directly related to the social network. The network constructed from communication data can only be considered as a proxy for the network of social relationships. Here we apply a systematic method, based on multiple hypothesis testing, to statistically validate the links and then construct the corresponding Bonferroni network, generalized to the directed case. We study two large datasets of mobile phone records, one from Europe and the other from China. For both datasets we compare the raw data networks with the corresponding Bonferroni networks and point out significant differences in the structures and in the basic network measures. We show evidence that the Bonferroni network provides a better proxy for the network of social interactions than the original one. By using the filtered networks we investigated the statistics and temporal evolution of small directed 3-motifs and conclude that closed communication triads have a formation time-scale, which is quite fast and typically intraday. We also find that open communication triads preferentially evolve to other open triads with a higher fraction of reciprocated calls. These stylized facts were observed for both datasets., Comment: 19 pages, 8 figures, 5 tables

Mobile phone calling is one of the most widely used communication methods in modern society. The records of calls among mobile phone users provide us a valuable proxy for the understanding of human communication patterns embedded in social networks. Mobile phone users call each other forming a directed calling network. If only reciprocal calls are considered, we obtain an undirected mutual calling network. The preferential communication behavior between two connected users can be statistically tested and it results in two Bonferroni networks with statistically validated edges. We perform a comparative analysis of the statistical properties of these four networks, which are constructed from the calling records of more than nine million individuals in Shanghai over a period of 110 days. We find that these networks share many common structural properties and also exhibit idiosyncratic features when compared with previously studied large mobile calling networks. The empirical findings provide us an intriguing picture of a representative large social network that might shed new lights on the modelling of large social networks.