The log-periodic-AR(1)-GARCH(1,1) model for financial crashes

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.     

Network topology of an experimental futures exchange

Many systems of different nature exhibit scale free behaviors. Economic systems with power law distribution in the wealth are one of the examples. To better understand the working behind the complexity, we undertook an experiment recording the interactions between market participants. A Web server was setup to administer the exchange of futures contracts whose liquidation prices were coupled to event outcomes. After free registration, participants started trading to compete for the money prizes upon maturity of the futures contracts at the end of the experiment. The evolving `cash' flow network was reconstructed from the transactions between players. We show that the network topology is hierarchical, disassortative and small-world with a power law exponent of 1.02±0.09 in the degree distribution after an exponential decay correction. The small-world property emerged early in the experiment while the number of participants was still small. We also show power law-like distributions of the net incomes and inter-transaction time intervals. Big winners and losers are associated with high degree, high betweenness centrality, low clustering coefficient and low degree-correlation. We identify communities in the network as groups of the like-minded. The distribution of the community sizes is shown to be power-law distributed with an exponent of 1.19±0.16.     

Correlation based networks of equity returns sampled at different time horizons

We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001–2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.     

Universal scaling behaviour in weighted trade networks

Identifying universal patterns in complex economic systems can reveal the dynamics and organizing principles underlying the process of system evolution. We investigate the scaling behaviours that have emerged in the international trade system by describing them as a series of evolving weighted trade networks. The maximum-flow spanning trees (constructed by maximizing the total weight of the edges) of these networks exhibit two universal scaling exponents: (1) topological scaling exponent η = 1.30 and (2) flow scaling exponent ζ = 1.03.     

Self-organizing Ising model of financial markets

We study a dynamical Ising-like model of agents' opinions (buy or sell) with learning, in which the coupling coefficients are re-assessed continuously in time according to how past external news (time-varying magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we find that the stylized facts of financial markets are reproduced only when agents misattribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the Ising critical point.     

Roughness and finite size effect in the NYSE stock-price fluctuations

We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effects which alter the apparent Hurst (H) exponent. We show, by analytical methods, that finite size effects always lead to an enhancement of H. We then consider the effect of fat tails on the analysis of the roughness and show that the finite size effects are strongly enhanced by the fat tails. The non stationarity of the stock price dynamics also enhances the finite size effects which, in principle, can become important even in the asymptotic regime. We then compute the Hurst exponent for a set of stocks of the NYSE and argue that the interpretation of the value of H is highly ambiguous in view of the above results. Finally we propose an alternative determination of the roughness in terms of the fluctuations from moving averages with variable characteristic times. This permits to eliminate most of the previous problems and to characterize the roughness in useful way. In particular this approach corresponds to the automatic elimination of trends at any scale.     

Statistical regularities in the return intervals of volatility

We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets. In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series. We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 0.6 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day). Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies. We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, ℓ<ℓ^* with α₁=0.64±0.02 and ℓ> ℓ^* with α₂=0.92±0.04; these exponent values are similar to results of Liu et al. for the volatility. As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk.     

World currency exchange rate cross-correlations

World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998–May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.     

Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.     

肺部超声、机械功与重症肺炎肺水肿及ARDS关系分析

回顾性选取95例重症肺炎(SP)患者,根据是否发生急性呼吸窘迫综合征(ARDS)分为ARDS组(n=38)、无ARDS组(n=57),比较两组治疗前、治疗24 h后、治疗48 h后肺部超声评分(LUS)、机械功(MP),比较不同LUS评分、MP水平者肺水肿发生率,采用Spearman分析LUS评分、MP与ARDS严重程度关系,采用多因素Logistic回归方程分析ARDS的相关影响因素,采用受试者操作特征(ROC)曲线及ROC曲线下面积(AUC)分析各指标的预测价值。结果显示,ARDS组治疗24 h、48 h后LUS评分、MP高于无ARDS组(P<0.05);LUS评分、MP高水平者肺水肿发生率高于低水平者(P<0.05);治疗24 h、48 h后LUS评分、MP与ARDS发病及其严重程度呈正相关(P<0.05);治疗24 h、48 h后LUS评分联合MP预测ARDS的AUC分别为0.874、0.915(P<0.05)。提示LUS评分、MP有助于反映SP患者肺水肿发生风险,联合上述指标可为临床预测ARDS提供参考。