Wen-Jie Xie

Calling patterns in human communication dynamics

Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the cr-th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users.

Systemic risk and spatiotemporal dynamics of the US housing market

Housing markets play a crucial role in economies and the collapse of a real-estate bubble usually destabilizes the financial system and causes economic recessions. We investigate the systemic risk and spatiotemporal dynamics of the US housing market (1975–2011) at the state level based on the Random Matrix Theory (RMT). We identify richer economic information in the largest eigenvalues deviating from RMT predictions for the housing market than for stock markets and find that the component signs of the eigenvectors contain either geographical information or the extent of differences in house price growth rates or both. By looking at the evolution of different quantities such as eigenvalues and eigenvectors, we find that the US housing market experienced six different regimes, which is consistent with the evolution of state clusters identified by the box clustering algorithm and the consensus clustering algorithm on the partial correlation matrices. We find that dramatic increases in the systemic risk are usually accompanied by regime shifts, which provide a means of early detection of housing bubbles.

Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application

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.

Testing the weak-form efficiency of the WTI crude oil futures market

The weak-form efficiency of energy futures markets has long been studied and empirical evidence suggests controversial conclusions. In this work, nonparametric methods are adopted to estimate the Hurst indexes of the WTI crude oil futures prices (1983–2012) and a strict statistical test in the spirit of bootstrapping is put forward to verify the weak-form market efficiency hypothesis. The results show that the crude oil futures market is efficient when the whole period is considered. When the whole series is divided into three sub-series separated by the outbreaks of the Gulf War and the Iraq War, it is found that the Gulf War reduced the efficiency of the market. If the sample is split into two sub-series based on the signing date of the North American Free Trade Agreement, the market is found to be inefficient in the sub-periods during which the Gulf War broke out. The same analysis on short-time series in moving windows shows that the market is inefficient only when some turbulent events occur, such as the oil price crash in 1985, the Gulf war, and the oil price crash in 2008.

Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index

Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst indexes H∈(0,1). Special attention has been paid to the impact of the Hurst index on topological properties. It is found that the clustering coefficient C decreases when H increases. We also found that the mean length L of the shortest paths increases exponentially with H for fixed length N of the original time series. In addition, L increases linearly with respect to N when H is close to 1 and in a logarithmic form when H is close to 0. Although the occurrence of different motifs changes with H, the motif rank pattern remains unchanged for different H. Adopting the node-covering box-counting method, the horizontal visibility graphs are found to be fractals and the fractal dimension dB decreases with H. Furthermore, the Pearson coefficients of the networks are positive and the degree–degree correlations increase with degree, which indicate that the horizontal visibility graphs are assortative. With the increase of H, the Pearson coefficient decreases first and then increases, in which the turning point is around H=0.6. The presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional Brownian motions is different from many cases where fractal networks are usually disassortative.

Extreme value statistics and recurrence intervals of NYMEX energy futures volatility

Energy markets and the associated energy futures markets play a crucial role in global economies. It is of great theoretical and practical significance to gain a deeper understanding of extreme value statistics of the volatility of energy futures traded on the New York Mercantile Exchange (NYMEX). We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times τ between consecutive volatilities exceeding a given threshold q. We find that the recurrence intervals are distributed as a stretched exponential Pqτ∼eaτ−γ, where the exponent γ decreases with increasing q, and there is no scaling behavior in the distributions for different thresholds q after the recurrence intervals are scaled with the mean recurrence interval τ¯. These findings are significant under the Kolmogorov–Smirnov test and the Cramer–von Mises test. We show that the empirical estimations are in nice agreement with the numerical integration results for the occurrence probability Wq(Δt|t) of a next event above the threshold q within a (short) time interval after an elapsed time t from the last event above q. We also investigate the memory effects of the recurrence intervals. It is found that the conditional distributions of large and small recurrence intervals differ from each other and the conditional mean of the recurrence intervals scale as a power law of the preceding interval τ¯τ0/τ¯∼τ0/τ¯β, indicating that the recurrence intervals have short-term correlations. Detrended fluctuation analysis and detrending moving average analysis further uncover that the recurrence intervals possess long-term correlations. We confirm that the “clustering” of the volatility recurrence intervals is caused by the long-term correlations well known to be present in the volatility. Our findings shed new lights on the behavior of large volatilities and have potential implications in risk management of energy futures.

A comparative analysis of the statistical properties of large mobile phone calling networks

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.

Unveiling correlations between financial variables and topological metrics of trading networks: Evidence from a stock and its warrant

Traders develop and adopt different trading strategies attempting to maximize their profits in financial markets. These trading strategies not only result in specific topological structures in trading networks, which connect the traders with the pairwise buy–sell relationships, but also have potential impacts on market dynamics. Here, we present a detailed analysis on how the market behaviors are correlated with the structures of traders in trading networks based on audit trail data for the Baosteel stock and its warrant at the transaction level from 22 August 2005 to 23 August 2006. In our investigation, we divide each trade day into 48 rolling time windows with a length of 5 min, construct a trading network within each window, and obtain a time series of over 11,600 trading networks. We find that there are strongly simultaneous correlations between the topological metrics (including network centralization, assortative index, and average path length) of trading networks that characterize the patterns of order execution and the financial variables (including return, volatility, intertrade duration, and trading volume) for the stock and its warrant. Our analysis may shed new lights on how the microscopic interactions between elements within complex system affect the system’s performance.

Club convergence of house prices: Evidence from China’s ten key cities

The latest global financial tsunami and its follow-up global economic recession has uncovered the crucial impact of housing markets on financial and economic systems. The Chinese stock market experienced a markedly fall during the global financial tsunami and Chinas economy has also slowed down by about 2\%-3\% when measured in GDP. Nevertheless, the housing markets in diverse Chinese cities seemed to continue the almost nonstop mania for more than ten years. However, the structure and dynamics of the Chinese housing market are less studied. Here we perform an extensive study of the Chinese housing market by analyzing ten representative key cities based on both linear and nonlinear econophysical and econometric methods. We identify a common collective driving force which accounts for 96.5\% of the house price growth, indicating very high systemic risk in the Chinese housing market. The ten key cities can be categorized into clubs and the house prices of the cities in the same club exhibit an evident convergence. These findings from different methods are basically consistent with each other. The identified city clubs are also consistent with the conventional classification of city tiers. The house prices of the first-tier cities grow the fastest, and those of the third- and fourth-tier cities rise the slowest, which illustrates the possible presence of a ripple effect in the diffusion of house prices in different cities.

Trading networks, abnormal motifs and stock manipulation

We study trade-based manipulation of stock prices from the perspective of complex trading networks constructed by using detailed information of trades. A stock trading network consists of nodes and directed links, where every trader is a node and a link is formed from one trader to the other if the former sells shares to the latter. Specifically, three abnormal network motifs are investigated, which are found to be formed by a few traders, implying potential intention of price manipulation. We further investigate the dynamics of volatility, trading volume, average trade size and turnover around the transactions associated with the abnormal motifs for large, medium and small trades. It is found that these variables peak at the abnormal events and exhibit a power-law accumulation in the pre-event time period and a power-law relaxation in the post-event period. We also find that the cumulative excess returns are significantly positive after buyer-initiated suspicious trades and exhibit a mild price reversal after seller-initiated suspicious trades. These findings can be better understood in favour of price manipulation. Our work sheds new lights into the detection of price manipulation resorting to the abnormal motifs of complex trading networks.