arXiv subjects

Wei-Xing Zhou

Publications and source records attributed to Wei-Xing Zhou.

191 records · Page 11Linked to original sources

arXiv2005

Importance of Positive Feedbacks and Over-confidence in a Self-Fulfilling Ising Model of Financial Markets

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are over-confident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

cond-mat.stat-mech↗

arXiv2005

Shape complexity and fractality of fracture surfaces of swelled isotactic polypropylene with supercritical carbon dioxide

We have investigated the fractal characteristics and shape complexity of the fracture surfaces of swelled isotactic polypropylene Y1600 in supercritical carbon dioxide fluid through the consideration of the statistics of the islands in binary SEM images. The distributions of area $A$, perimeter $L$, and shape complexity $C$ follow power laws $p(A)\sim A^{-(μ_A+1)}$, $p(L)\sim L^{-(μ_L+1)}$, and $p(C)\sim C^{-(ν+1)}$, with the scaling ranges spanning over two decades. The perimeter and shape complexity scale respectively as $L\sim A^{D/2}$ and $C\sim A^q$ in two scaling regions delimited by $A\approx 10^3$. The fractal dimension and shape complexity increase when the temperature decreases. In addition, the relationships among different power-law scaling exponents $μ_A$, $μ_B$, $ν$, $D$, and $q$ have been derived analytically, assuming that $A$, $L$, and $C$ follow power-law distributions.

cond-mat.stat-mech↗

arXiv2004

Inverse statistics in stock markets: Universality and idiosyncracy

Investigations of inverse statistics (a concept borrowed from turbulence) in stock markets, exemplified with filtered Dow Jones Industrial Average, S&P 500, and NASDAQ, have uncovered a novel stylized fact that the distribution of exit time follows a power law $p(τ_ρ) \sim τρ^{-α}$ with $α\approx 1.5$ at large $τ_ρ$ and the optimal investment horizon $τ_ρ^*$ scales as $ρ^γ$ [1-3]. We have performed an extensive analysis based on unfiltered daily indices and stock prices and high-frequency (5-min) records as well in the markets all over the world. Our analysis confirms that the power-law distribution of the exit time with an exponent of about $α=1.5$ is universal for all the data sets analyzed. In addition, all data sets show that the power-law scaling in the optimal investment horizon holds, but with idiosyncratic exponent. Specifically, $γ\approx 1.5$ for the daily data in most of the developed stock markets and the five-minute high-frequency data, while the $γ$ values of the daily indexes and stock prices in emerging markets are significantly less than 1.5. We show that there is of little chance that this discrepancy in $γ$ stems from the difference of record sizes in the two kinds of stock markets.

cond-mat.other↗

arXiv2004

Does randomness in multifractals imply latent dimensions?

Negative, or latent, dimensions have always attracted a strong interest since their discovery. When randomness is introduced in multifractals, the sample-to-sample fluctuations of multifractal spectra emerge inevitably, which has motivated various studies in this field. In this work, we study a class of multinomial measures and argue the asymptotic behaviors of the multifractal function as . The so-called latent dimensions condition (LDC) is presented which states that latent dimensions may be absent in discrete random multinomial measures. In order to clarify the discovery, several examples are illustrated.

cond-mat.stat-mech↗

arXiv2004

Multifractality of Drop Breakup in Air-blast Nozzle Atomization Process

The multifractal nature of drop breakup in air-blast nozzle atomization process has been studied. We apply the multiplier method to extract the negative and the positive parts of the f(alpha) curve with the data of drop size distribution measured using Dual PDA. A random multifractal model with the multiplier triangularly distributed is proposed to characterize the breakup of drops. The agreement of the left part of the multifractal spectra between the experimental result and the model is remarkable. The cause of the distinction of the right part of the f(alpha) curve is argued. The fact that negative dimensions arise in the current system means that the spatial distribution of the drops yielded by the high-speed jet fluctuates from sample to sample. On other words, the spatial concentration distribution of the disperse phase in the spray zone fluctuates momentarily showing intrinsic randomness.

cond-mat.stat-mech↗

arXiv2002

Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes

We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the so-called (H,q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(t_c-t) variable, where t_c is the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency $f = 1.02 \pm 0.05$ corresponding to the scaling ratio $λ= 2.67 \pm 0.12$. These values are in very good agreement with those obtained in past works with different parametric techniques.

cond-mat.stat-mech↗

arXiv2002

Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures

We introduce a generalization of the q-analysis, which provides a novel non-parametric tool for the description and detection of log-periodic structures associated with discrete scale invariance. We use this generalized q-analysis to construct a signature called the (H,q)-derivative of discrete scale invariance, which we use to detect the log-periodicity in the energy release rate and its cumulative preceding the rupture of five pressure tanks made of composite carbon-matrix material. We investigate the significance level of the spectral Lomb periodogram of the optimal (H,q)-derivative. We confirm and strengthen previous parametric results that the energy release rate and it cumulative exhibit log-periodicity before rupture. However, our tests to use this method as a scheme for the prediction of the critical value of the stress at rupture are not encouraging.

cond-mat.stat-mech↗

arXiv2001

Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

We present the results of a search of log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (2500) of three-dimensional fully developed turbulence. A simple dynamical representation of the Richardson-Kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log-periodic corrections to scaling associated with a discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical'' averaging that we test extensively on synthetic examples constructed to mimick the interplay between a weak log-periodic component and rather strong multiplicative and phase noises. Our extensive tests confirm the remarkable observation of statistically significant log-periodic corrections to scaling, with a prefered scaling ratio for length scales compatible with the value gamma = 2. A strong confirmation of this result is provided by the identification of up to 5 harmonics of the fundamental log-periodic undulations, associated with up to 5 levels of the underlying hierarchical dynamical structure. A natural interpretation of our results is that the Richardson-Kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales.

cond-mat.stat-mech↗

arXiv2001

Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise

We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. We investigate general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the second highest Lomb peak to the maximum peak. Using the insight obtained by the present statistical study, we re-examine previously reported claims of ``log-periodicity'' and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

cond-mat.stat-mech↗

arXiv2001

Features arising from randomly multiplicative measures

Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically. In these two illustrations branching emerges in the curve of generalized dimensions, and more abnormally, negative values of generalized dimensions arise. Therefore, we classify the random multifractal measures into three classes based on the discrepancy between the curves of generalized dimensions. Other equivalent classifications are also presented.... We apply the cascade processes studied in this paper to characterize two stochastic processes, i.e., the energy dissipation field in fully developed turbulence and the droplet breakup in atomization. The agreement between the proposed model and the experiments are remarkable.

nlin.AO↗

arXiv2000

On the properties of random multiplicative measures with the multipliers exponentially distributed

Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with their multipliers satisfying exponentially distributed is investigated in detail. Branching emerges in the curve of generalized dimensions, and negative values of generalized dimensions arise. Three equivalent methods of classification of the random multifractal measures are proposed, which is based on: (i) the discrepancy between the curves of generalized dimensions, (ii) the solution properties of equation T(qcrit) =0, and (iii) the relative position of the curve f(alpha) and the diagonal f(alpha)=alpha in the first quadrant. These three classes correspond to μ([0,1])=infinity, μ([0,1])=1 and μ([0,1])=0, respectively. Phase diagram is introduced to illustrate the diverse performance of the random measures that is multiplicatively generated.

nlin.AO↗