Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007–2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.     

多层石墨烯的表面起伏的分子动力学模拟

运用经典分子动力学方法,研究了呈现不同堆积方式的多层石墨烯在不同温度下的表面起伏,并且和单层、双层石墨烯做对比,计算发现:室温下,多层石墨烯中存在着横向特征尺寸约为100 A的起伏,该尺寸会随着温度的升高而增大;同时,起伏的高度也随着温度的升高而增大,这些石墨烯的层内起伏高度关联函数都遵从幂指数标度行为G_h(q)αq~(-α),对于同一种石墨烯,温度越高幂指数越小;而在同一温度下,不同堆积方式的石墨烯的幂指数也不同,所有这些特征都来源于温度以及层间耦合作用引起的非谐效应。     

二维完全阻挫$lt;i$gt;XY$lt;/i$gt;模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless（KT）型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上（T>T_KT）,独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下（T<T_KT）测量的结果一致. 关键词： 蒙特卡罗法 动力学指数 Kosterlitz-Thouless相变 XY模型')" href="#">二维完全阻挫XY模型     

Multifractal detrended fluctuation analysis of sheep livestock prices in origin

The multifractal detrended fluctuation analysis (MF-DFA) is used to verify whether or not the returns of time series of prices paid to farmers in original markets can be described by the multifractal approach. By way of example, 5 weekly time series of prices of different breeds, slaughter weight and market differentiation from 2000 to 2012 are analyzed. Results obtained from the multifractal parameters and multifractal spectra show that the price series of livestock products are of a multifractal nature. The Hurst exponent shows that these time series are stationary signals, some of which exhibit long memory (Merino milk-fed in Seville and Segureña paschal in Jaen), short memory (Merino paschal in Cordoba and Segureña milk-fed in Jaen) or even are close to an uncorrelated signals (Merino paschal in Seville). MF-DFA is able to discern the different underlying dynamics that play an important role in different types of sheep livestock markets, such as degree and source of multifractality. In addition, the main source of multifractality of these time series is due to the broadness of the probability function, instead of the long-range correlation properties between small and large fluctuations, which play a clearly secondary role.     

Non-stationary multifractality in stock returns

We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry et al. [E. Bacry, J. Delour, J.-F. Muzy, Multifractal random walk, Physical Review E 64 (2) (2001) 026103]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data are not in agreement with a MRW with constant intermittency parameter. We test these hypotheses of constant multifractality considering different specifications of MRW model with fatter tails: in all cases considered, although the thickness of the tails accounts for most of the anomalous fluctuations of multifractality, it still cannot fully explain the observed fluctuations.     

Auto-correlated behavior of WTI crude oil volatilities: A multiscale perspective

In this paper, we investigate the long-range auto-correlated behavior of WTI crude oil volatility series employing multifractal detrended fluctuation analysis. Our findings show that the for small time scales, the auto-correlations of volatilities were multifractal while for large time scales, the auto-correlations were nearly monofractal. Based on multiscale analysis, we also investigate the dynamics of auto-correlations for different intervals of time scales and find that several shocks could make significant effects on the auto-correlated behaviors for small time scales. Analyzing the dynamics of multifractality degrees of auto-correlations for small time scales, we find that the stronger auto-correlations were always related to the lower degrees of multifractality. At last, we have discussions on the determination factors of price behavior, the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long-range auto-correlations of volatility were always strong for both small time scales and large time scales. Our results are very important theoretically and practically.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

Long-range dependence in North Atlantic sea level

Sea level is an important parameter in climate and oceanographic applications. In this work the scaling behavior of sea level is analyzed from time series of sea level observations. The wavelet domain is particularly attractive for the identification of scaling behavior in an observed time series. The wavelet spectrum from a scale-by-scale wavelet analysis of variance reproduces in the wavelet domain the power laws underlying a scaling process, allowing the estimation of the scaling exponent from the slope of the wavelet spectrum. Here the scaling exponent is estimated in the wavelet domain for time series of sea level observations in the North Atlantic: at coastal sites from tide gauges, covering 50 years of monthly measurements, and in the open ocean from satellite altimetry, covering 12 years of satellite measurements at 10 days intervals. Both tide gauge and altimetry time series exhibit scaling behavior. Furthermore, the degree of stochastic persistence is spatially coherent and distinct at the coast and in the open ocean. Near the coast, the stochastic structure of the sea level observations is characterized by long-range dependence with a moderate degree of persistence. Larger values of the scaling exponent, consistent with weaker persistence, are concentrated in the northern Atlantic. At mid-latitudes the stochastic dependence of sea level observations is characterized by strong persistence in the form of strong long-range and 1/f dependence.     

Using models with long-term persistence to interpret the rapid increase of Earth’s temperature

Statistical processes with long-term persistence (LTP) offer a promising approach to modeling the natural dynamics of Earth’s temperature. One such process, the family of 1/f-noises, is used here to assess the plausibility of a natural origin for recent global warming. Following earlier studies, a model of natural variability with LTP is parameterized via paleoclimate reconstructions. The method developed here resolves a number of limitations in existing studies, primarily the problem of inaccuracies in estimating the spectral exponent of LTP. The output of the model is compared with the observed rate of temperature rise (0.61 ^°C/century between 1850 and 2007 for Northern hemispheric land air temperatures). We find that rates comparable with the observed global warming are very rarely generated by the model of natural variability (the probability is less than 2.3×10⁻⁴). Thus, natural agencies are not a plausible explanation for the observed global warming unless all the paleoclimate reconstructions through which the model is parameterized are underestimating natural variance by a factor of at least four.     

Multifractality in stock indexes: Fact or Fiction?

Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P 500, and NASDAQ) to check whether the indexes (instead of the returns) possess multifractality. We find that the mass exponent τ(q) is linear and the singularity α(q) is close to 1 for all trading days and all indexes. Furthermore, we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series. Hence, the so-called multifractality in the intraday stock market indexes is merely an illusion.     

Multifractal character of surface latent heat flux

Surface latent heat flux (SLHF) has been associated with the study of natural hazards, such as earthquakes and hurricanes and has been proposed as a useful quantity in the prediction and monitoring of their evolution. In the present study the Mediterranean Sea, parts of Europe, Africa and Turkey are mapped with regard to the multifractal characteristics of SLHF time series during a period of eight years (1997–2004). The estimated Hurst exponents are markedly larger over land than over sea. In the case of land, SLHF has the characteristics of a mean-averting process, while its records are over sea noticeably uncorrelated. In contrast to the rather monofractal and weak multifractal character observed in most regions, with the application of a detrended fluctuation analysis, intense multifractality is seen mainly in North Africa. Crossover segments are present in the scaling of negative moments, implying that the small SLHF fluctuations are affected by seasonal components. Identification of anomalous SLHF deviations from their long-term multifractal behavior may serve as a precursor of extreme atmospheric phenomena.     

Time-varying Hurst exponent for US stock markets

In this work, the dynamical behavior of the US stock markets is characterized on the basis of the temporal variations of the Hurst exponent estimated with detrended fluctuation analysis (DFA) over moving windows for the historical Dow Jones (1928-2007) and the S&P-500 (1950-2007) daily indices. According to the results drawn: (i) the Hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior, (ii) the major breakthrough of the long-term trend of the scaling behavior occurred in 1972, at the end of the Bretton Woods system, when the Hurst exponent shifted form a positive to a negative long-term trend. Other effects, such as the 1987 crisis and the emergence of anti-correlated behavior in the recent two years, are also discussed.     

Scaling in nature: from DNA through heartbeats to weather.

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.     

A multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in Tehran stock market

Employing the multifractal detrended fluctuation analysis (MF-DFA), the multifractal properties of trading behavior of individual and institutional traders in the Tehran Stock Exchange (TSE) are numerically investigated. Using daily trading volume time series of these two categories of traders, the scaling exponents, generalized Hurst exponents, generalized fractal dimensions and singularity spectrum are derived. Furthermore, two main sources of multifractality, i.e. temporal correlations and fat-tailed probability distributions are also examined. We also compare our results with data of S&P 500. Results of this paper suggest that for both classes of investors in TSE, multifractality is mainly due to long-range correlation while for S&P 500, the fat-tailed probability distribution is the main source of multifractality.     

Global climate models violate scaling of the observed atmospheric variability

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyze temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.     

Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA

We utilized asymmetric multifractal detrended fluctuation analysis in this study to examine the asymmetric multifractal scaling behavior of Chinese stock markets with uptrends or downtrends. Results show that the multifractality degree of Chinese stock markets with uptrends is stronger than that of Chinese stock markets with downtrends. Correlation asymmetries are more evident in large fluctuations than in small fluctuations. By discussing the source of asymmetric multifractality, we find that multifractality is related to long-range correlations when the market is going up, whereas it is related to fat-tailed distribution when the market is going down. The main source of asymmetric scaling behavior in the Shanghai stock market are long-range correlations, whereas that in the Shenzhen stock market is fat-tailed distribution. An analysis of the time-varying feature of scaling asymmetries shows that the evolution trends of these scaling asymmetries are similar in the two Chinese stock markets. Major financial and economical events may enhance scaling asymmetries.     

Different scaling behaviors in daily temperature records over China

Long-range correlations of five kinds of daily temperature records (i.e. daily average temperature records, daily maximum temperature records, daily minimum temperature records, diurnal temperature range and the sum of daily maximum and minimum temperature records) from 164 weather stations over China during 1951-2004 are analyzed by means of detrended fluctuation analysis (DFA). These five kinds of fluctuation series are found to be power-law correlated with scaling exponents larger than 0.5. Local changes of scaling exponents are examined and the spatial distributions of these different kinds of temperature records are similar except the diurnal temperature range (DTR for short) records. Furthermore, the differences of the scaling behavior among diurnal temperature records and other kinds of temperature records are discussed.     

Temporal-spatial diversities of long-range correlation for relative humidity over China

Long-range correlations of daily relative humidity anomaly records from 191 weather stations over China during 1951-2000 are analyzed by means of fluctuation analysis (FA) and detrended fluctuation analysis (DFA). The information about trends in the relative humidity records can be obtained by comparing the FA curve with DFA curves. The daily relative humidity fluctuations are found to be power-law correlated and their average scaling exponent is higher than that of the temperature fluctuations, indicating that the relative humidity fluctuations take different statistical behavior from other meteorological quantities and there exists a stronger persistence in the relative humidity fluctuations. Furthermore, it is also found that these power-law scaling properties vary from station to station and show both spatial and temporal diversities, which may be explained by a proposed mechanism.     

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T _g , the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T _g , revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.     

Hurst exponent footprints from activities on a large structural system

This paper presents Hurst exponent footprints from pseudo-dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring. The system is interesting due to associated uncertainty in large-scale structures and significant presence of human intervention arising from fundamentally different processes. Investigations into the variation of computed Hurst exponents on time series of limited lengths are carried out in this regard. The Hurst exponents are compared with respect to specific events during the rehabilitation, as well as with the data collection locations. The variations of local Hurst exponents about the values computed for each activity are presented. The scaling of Hurst exponents for different activities is also investigated; these are representative of the extent of multifractality for each event. The extent of multifractality is assessed along with its source and time dependency.