arXiv subjects

Wei-Xing Zhou

Publications and source records attributed to Wei-Xing Zhou.

At least 145 records · Page 8Linked to original sources

arXiv2010

Analyzing the prices of the most expensive sheet iron all over the world: Modeling, prediction and regime change

The private car license plates issued in Shanghai are bestowed the title of "the most expensive sheet iron all over the world", more expensive than gold. A citizen has to bid in an monthly auction to obtain a license plate for his new private car. We perform statistical analysis to investigate the influence of the minimal price $P_{\min}$ of the bidding winners, the quota $N_{\rm{quota}}$ of private car license plates, the number $N_{\rm{bidder}}$ of bidders, as well as two external shocks including the legality debate of the auction in 2004 and the auction regime reform in January 2008 on the average price $P_{\rm{mean}}$ of all bidding winners. It is found that the legality debate of the auction had marginal transient impact on the average price in a short time period. In contrast, the change of the auction rules has significant permanent influence on the average price, which reduces the price by about 3020 yuan Renminbi. It means that the average price exhibits nonlinear behaviors with a regime change. The evolution of the average price is independent of the number $N_{\rm{bidder}}$ of bidders in both regimes. In the early regime before January 2008, the average price $P_{\rm{mean}}$ was influenced only by the minimal price $P_{\min}$ in the preceding month with a positive correlation. In the current regime since January 2008, the average price is positively correlated with the minimal price and the quota in the preceding month and negatively correlated with the quota in the same month. We test the predictive power of the two models using 2-year and 3-year moving windows and find that the latter outperforms the former. It seems that the auction market becomes more efficient after the auction reform since the prediction error increases.

q-fin.ST↗

arXiv2009

Finite-size effect and the components of multifractality in financial volatility

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.

q-fin.ST↗

arXiv2009

Superfamily classification of nonstationary time series based on DFA scaling exponents

The superfamily phenomenon of time series with different dynamics can be characterized by the motif rank patterns observed in the nearest-neighbor networks of the time series in phase space. However, the determinants of superfamily classification are unclear. We attack this problem by studying the influence of linear temporal correlations and multifractality using fractional Brownian motions (FBMs) and multifractal random walks (MRWs). Numerical investigations unveil that the classification of superfamily phenomenon is uniquely determined by the detrended fluctuation analysis (DFA) scaling exponent $α$ of the time series. Only four motif patterns are observed in the simulated data, which are delimited by three DFA scaling exponents $α\simeq 0.25$, $α\simeq 0.35$ and $α\simeq 0.45$. The validity of the result is confirmed by stock market indexes and turbulence velocity signals.

q-fin.ST↗

arXiv2009

Scaling and memory in the non-poisson process of limit order cancelation

The order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order-driven markets. We investigate the dynamics of order cancelation by studying the statistical properties of inter-cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the Shenzhen Stock Exchange of China in year 2003. Three types of cancelations are considered including cancelation of any limit orders, of buy limit orders and of sell limit orders. We find that the distributions of the inter-cancelation durations of individual stocks can be well modeled by Weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks. Complex intraday patterns are also unveiled in the inter-cancelation durations. The detrended fluctuation analysis (DFA) and the multifractal DFA show that the inter-cancelation durations possess long-term memory and multifractal nature, which are not influenced by the intraday patterns. No clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale. These findings indicate that the cancelation of limit orders is a non-Poisson process, which has potential worth in the construction of order-driven market models.

q-fin.TR↗

arXiv2009

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 $Δα$ of the multifractal spectrum while the fat tails have major impact on $Δα$, which confirms the earlier results. In addition, the linear correlation is found to have only a horizontal translation effect on the multifractal spectrum in which the distance is approximately equal to the difference between its DFA scaling exponent and 0.5. Our method can also be applied to other financial or physical variables and other multifractal formalisms.

q-fin.ST↗

arXiv2009

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.

q-fin.ST↗

arXiv2009

Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors. There are marked discrepancies in the allometric scaling behaviors between the stock indices and the Brownian motions. Using surrogate time series, we find that these discrepancies are caused by the fat-tailedness of the return distribution, the nonlinear long-term correlation, and a coupling effect between these two influence factors.

q-fin.ST↗

arXiv2009

Recurrence interval analysis of high-frequency financial returns and its application to risk estimation

We investigate the probability distributions of the recurrence intervals $τ$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures including the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cramér-von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds $q$. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability $W_q(Δ{t},t)$, Value-at-Risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.

q-fin.ST↗

arXiv2009

Scaling and memory in the return intervals of realized volatility

We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold $q$ are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent $γ$ and the threshold $q$. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility.

q-fin.ST↗

arXiv2009

Online-offline activities and game-playing behaviors of avatars in a massive multiplayer online role-playing game

Massive multiplayer online role-playing games (MMORPGs) are very popular in China, which provides a potential platform for scientific research. We study the online-offline activities of avatars in an MMORPG to understand their game-playing behavior. The statistical analysis unveils that the active avatars can be classified into three types. The avatars of the first type are owned by game cheaters who go online and offline in preset time intervals with the online duration distributions dominated by pulses. The second type of avatars is characterized by a Weibull distribution in the online durations, which is confirmed by statistical tests. The distributions of online durations of the remaining individual avatars differ from the above two types and cannot be described by a simple form. These findings have potential applications in the game industry.

physics.pop-ph↗

arXiv2009

Modified detrended fluctuation analysis based on empirical mode decomposition

Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMD-based DFA method. Similarly, we also propose a modified multifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process. We find that the EMD-based DFA method performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order $q$ of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the one-minute data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed.

cond-mat.stat-mech↗

arXiv2009

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.

q-fin.ST↗

arXiv2009

Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent $α$ is a linear function of the Hurst index $H$ of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from two Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the $α\sim H$ linear relationship.

physics.soc-ph↗

arXiv2009

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in opening call auction and the closing price of last trading day, is asymmetric and that the distribution displays a sharp peak at zero relative price and a relatively wide peak at negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a $q$-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.

q-fin.ST↗

arXiv2009

Statistical properties of online avatar numbers in a massive multiplayer online role-playing game

Massive multiplayer online role-playing games (MMORPGs) are very popular in past few years. The profit of an MMORPG company is proportional to how many users registered, and the instant number of online avatars is a key factor to assess how popular an MMORPG is. We use the on-off-line logs on an MMORPG server to reconstruct the instant number of online avatars per second and investigate its statistical properties. We find that the online avatar number exhibits one-day periodic behavior and clear intraday pattern, the fluctuation distribution of the online avatar numbers has a leptokurtic non-Gaussian shape with power-law tails, and the increments of online avatar numbers after removing the intraday pattern are uncorrelated and the associated absolute values have long-term correlation. In addition, both time series exhibit multifractal nature.

physics.soc-ph↗

arXiv2009

Long-term correlations and multifractal analysis of trading volumes for Chinese stocks

We investigate the temporal correlations and multifractal nature of trading volume of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the trading volume exhibit size-dependent non-universal long memory and multifractal nature. No crossover in the power-law dependence of the detrended fluctuation functions is observed. Our results show that the intraday pattern in the trading volume has negligible impact on the long memory and multifractality.

q-fin.ST↗

arXiv2008

Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence

We study the statistical properties of return intervals $r$ between successive energy dissipation rates above a certain threshold $Q$ in three-dimensional fully developed turbulence. We find that the distribution function $P_Q(r)$ scales with the mean return interval $R_Q$ as $P_Q(r)=R_Q^{-1}f(r/R_Q)$ except for $r=1$, where the scaling function $f(x)$ has two power-law regimes. The return intervals are short-term and long-term correlated and possess multifractal nature. The Hurst index of the return intervals decays exponentially against $R_Q$, predicting that rare extreme events with $R_Q\to\infty$ are also long-term correlated with the Hurst index $H_\infty=0.639$.

physics.flu-dyn↗

arXiv2008

Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the "$q$-Gamma" function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of trading volumes at different timescales $Δ{t}$ ranging from 1 min to 240 min can be well modeled. The applicability of the $q$-Gamma functions for multiple trades is restricted to the transaction numbers $Δ{n}\leqslant8$. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents $α$ of the distribution of trade sizes and trading volumes, we get $α>2$, well outside the L{é}vy regime.

q-fin.ST↗