Wei-Xing Zhou

Multifractal detrended cross-correlation analysis for two nonstationary signals

We propose a method called multifractal detrended cross-correlation analysis to investigate the multifractal behaviors in the power-law cross-correlations between two time series or higher-dimensional quantities recorded simultaneously, which can be applied to diverse complex systems such as turbulence, finance, ecology, physiology, geophysics, and so on. The method is validated with cross-correlated one- and two-dimensional binomial measures and multifractal random walks. As an example, we illustrate the method by analyzing two financial time series.

Prediction of Drug-Target Interactions and Drug Repositioning via Network-Based Inference

Drug-target interaction (DTI) is the basis of drug discovery and design. It is time consuming and costly to determine DTI experimentally. Hence, it is necessary to develop computational methods for the prediction of potential DTI. Based on complex network theory, three supervised inference methods were developed here to predict DTI and used for drug repositioning, namely drug-based similarity inference (DBSI), target-based similarity inference (TBSI) and network-based inference (NBI). Among them, NBI performed best on four benchmark data sets. Then a drug-target network was created with NBI based on 12,483 FDA-approved and experimental drug-target binary links, and some new DTIs were further predicted. In vitro assays confirmed that five old drugs, namely montelukast, diclofenac, simvastatin, ketoconazole, and itraconazole, showed polypharmacological features on estrogen receptors or dipeptidyl peptidase-IV with half maximal inhibitory or effective concentration ranged from 0.2 to 10 µM. Moreover, simvastatin and ketoconazole showed potent antiproliferative activities on human MDA-MB-231 breast cancer cell line in MTT assays. The results indicated that these methods could be powerful tools in prediction of DTIs and drug repositioning.

Discrete hierarchical organization of social group sizes

The ‘social brain hypothesis’ for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non–human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3–5, 9–15, 30–45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.

Detrending moving average algorithm for multifractals

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (θ=0), centered (θ=0.5), and forward (θ=1) detrending windows. We find that the estimated multifractal scaling exponent τ(q) and the singularity spectrum f(α) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

Multifractal detrending moving average cross-correlation analysis

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q<0 and underperforms when q>0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

The 2006–2008 oil bubble: Evidence of speculation, and prediction

D. Sornette, 2 R. Woodard, and W.-X. Zhou Chair of Entrepreneurial Risks, Department of Management, Technology and Economics, ETH Zurich, CH-8001 Zurich, Switzerland Swiss Finance Institute, c/o University of Geneva, 40 blvd. Du Pont dArve, CH 1211 Geneva 4, Switzerland School of Business, School of Science, Research Center for Econophysics and Research Center of Systems Engineering, East China University of Science and Technology, Shanghai 200237, China (Dated: December 2, 2008)

Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese Stock Market Bubbles

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competing with negative feedback spirals of crash expectations. We use the LPPL model in one of its incarnations to analyze two bubbles and subsequent market crashes in two important indexes in the Chinese stock markets between May 2005 and July 2009. Both the Shanghai Stock Exchange Composite and Shenzhen Stock Exchange Component indexes exhibited such behavior in two distinct time periods: 1) from mid-2005, bursting in Oct. 2007 and 2) from Nov. 2008, bursting in the beginning of Aug. 2009. We successfully predicted time windows for both crashes in advance with the same methods used to successfully predict the peak in mid-2006 of the US housing bubble and the peak in July 2008 of the global oil bubble. The more recent bubble in the Chinese indexes was detected and its end or change of regime was predicted independently by two groups with similar results, showing that the model has been well-documented and can be replicated by industrial practitioners. Here we present more detailed analysis of the individual Chinese index predictions and of the methods used to make and test them.

Detrended fluctuation analysis for fractals and multifractals in higher dimensions.

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MFDFA is also adopted to analyze two images from nature and experiment, and nice scaling laws are unraveled.

Is there a real-estate bubble in the US?

Using a methodology developed in previous papers, we analyze the quarterly average sale prices of new houses sold in the USA as a whole, in the Northeast, Midwest, South, and West of the USA, in each of the 50 states and the District of Columbia of the USA, to determine whether they have grown at a faster-than-exponential rate which we take as the diagnostic of a bubble. We find that 22 states (mostly Northeast and West) exhibit clear-cut signatures of a fast-growing bubble. From the analysis of the S&P 500 Home Index, we conclude that the turning point of the bubble will probably occur around mid-2006.

The components of empirical multifractality in financial returns

We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with those of four kinds of surrogate data: (1) shuffled data that contain no temporal correlation but have the same distribution, (2) surrogate data in which any nonlinear correlation is removed but the distribution and linear correlation are preserved, (3) surrogate data in which large positive and negative returns are replaced with small values, and (4) surrogate data generated from alternative fat-tailed distributions with the temporal correlation preserved. We find that all these factors have influence on the multifractal spectrum. We also find that the temporal structure (linear or nonlinear) has minor impact on the singularity width