Narrow Results

Applying the statistical hypothesis testing, we investigate several nonlinear properties embedded in the return series of the Chinese Fund Market (CFM), which suggests the series is non-normal, auto-correlative and heteroskedastic. We hereby analyze the Hurst exponent of the return series in different timescales on the basis of the detrended fluctuation analysis (DFA) algorithm, and discuss the fractal behavior of the CFM. Furthermore, by studying the correlation of different weights in the volatility, we find the persistent long-range power-law correlation exists in the time series. We also provide hints that the above statistical properties are insensitive to the funds kind, and may be irrelevant to the market phases. Our work may reveal the self-similarity characteristics of the financial market and show a better understanding of the CFM.

We consider the flow intensity of economic and financial news taken from a nine-month period of 2015. This data is found to be well approximated by a persistent self-affine walk. It is characterized by a Hurst exponent of $H>0.6$ over three orders of magnitude in time ranging from minutes to several days. In this paper, we use the Detrended Fluctuation Analysis (DFA) of order 1, Rescaled Range Analysis (R/S) and Fourier Transform Method (FTM) to examine long-range auto-correlation and self-similarity of time series of news flow intensity. DFA method allowed us to reveal a strong scaling behavior as well as to detect a distinct crossover effect. On the other hand, it turns out that for the classic R/S analysis and Fourier transform techniques, the scaling regimes and/or positions of cross-overs are hard to define.

In this paper, we can obtain a second conventional formula (${\mathrm{\text{CF}}}_{\mathrm{\text{II}}}$) with two components by extending the conventional formula ${\mathrm{\text{CF}}}_{\mathrm{\text{I}}}$ with one component for Bose–Einstein Correlation (BEC). We used ${\mathrm{\text{CF}}}_{\mathrm{\text{II}}}$ to analyze the BEC at $Z^0$-pole as part of the OPAL collaboration. $R_1(\mathrm{\text{G}})=0.91\pm 0.03$ fm (${\lambda }_1=0.61\pm 0.03$) and $R_2(\mathrm{\text{G}})=2.57\pm 0.44$fm (${\lambda }_1=0.35\pm 0.09$) are the estimated interaction region, where ${\lambda }_1$ and ${\lambda }_2$ are the degrees of coherence, and G is the Gaussian distribution, respectively. Long-range correlation (LRC) is also studied.

The L3 Collaboration reported data on 2-jet and 3-jet Bose–Einstein correlations (BECs) with the results obtained through the $\tau$-model in 2011. In this study, we analyze these correlations using the conventional formula with the Gaussian long-range correlation (${\mathrm{\text{CF}}}_{\mathrm{\text{I}}}\times {\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}$). The estimated ranges of interactions for 2-jet and 3-jet, $R_{\mathrm{\text{2-jet}}}$ and $R_{\mathrm{\text{3-jet}}}$, are almost the same magnitude as those by $\tau$-model: $R_{\mathrm{\text{2-jet}}}=0.83\pm 0.05$ (stat) fm and $R_{\mathrm{\text{3-jet}}}=1.09\pm 0.04$ (stat) fm. The anticorrelation in BEC (less than 1.0) observed by the L3 Collaboration is related to the partially negative density profile (${\rho }_{\tau ,\mathrm{\text{BE}}}(\xi )$ in $\xi$ space) in the $\tau$-model and the ${\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}=1/(1+\alpha e^{-\beta Q^2})$ in ${\mathrm{\text{CF}}}_{\mathrm{\text{I}}}\times {\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}$, respectively. Remarkably, the probability $P_{\tau }(\xi )$ calculated from the Levy canonical form exhibits partially negative behavior.

For matrix product states of one-dimensional spin-1/2 chains, we investigate the properties of quantum phase transition of the proposed composite system. We find that the system has three different ferromagnetic phases, one line of the two ferromagnetic phases coexisting equally describes the paramagnetic state, and the other two lines of two ferromagnetic phases coexisting equally describe the ferrimagnetic states, while the three phases coexisting equally point describes the ferromagnetic state. Whether on phase transition lines or at the phase transition point, the system is always in an isolated mediate-coupling state, the physical quantities are discontinuous and the system has long-range correlation and has long-range classical correlation and long-range quantum correlation. We believe that our work is helpful for comprehensively and profoundly understanding the quantum phase transitions, and of some certain guidance and enlightening on the classification and measure of quantum correlation of quantum many-body systems.

This paper studies the cross-correlation between the pseudorapidity and azimuthal distributions of the shower particles emitted in ${}^{32}$S-AgBr interactions at 200GeV and ${}^{16}$O-AgBr interactions at 60GeV applying Multifractal detrended cross-correlation analysis (MF-DXA) methodology. The cross-correlation between the pseudorapidity ($\eta$) space and the azimuthal ($\varphi$) space is found to exhibit multifractality in case of both the interactions. The results obtained from the analysis of the experimental data were compared with those obtained for the randomly shuffled data for both the interactions, and the results revealed that the multifractality is due to the presence of long-range correlations. The study clearly indicates that the strength of the cross-correlation depends on both the projectile mass and energy.

Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence) and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the standard deviation; scaling exponents describe how dispersions change with the time scale. Intermittency has been defined as a difference between two scaling exponents. After taking a moving average, these measures give descriptive information, even for short heart rate records. For this data, dispersion and intermittency perform better than scaling exponents.

Multifractal detrended fluctuation analysis (MF-DFA) method is applied to analyze the daily electric load time series. The results of the MF-DFA show that there are three crossover timescales at seven days, 15 days and 365 days approximately in the fluctuation function. Also we find that these fluctuations have multifractal nature with long range correlation behavior. The multifractal singularity spectrum of the daily electric load series has been fitted by the quadratic function model. Comparing the MF-DFA results of the original load series with those of shuffled and surrogate series, it concludes that the multifractal characteristics of the daily electric load time series is due to both broadness of the probability density function and long-range correlation, and the long-range correlation is dominant.

The (detrended cross-correlation analysis) DCCA cross-correlation coefficient was proposed to measure the level of long-range cross-correlations between two non-stationary time series on multiple time scales. It has been applied to diverse areas of interest, although many properties of this method are not clear. In this paper, we theoretically study several fundamental properties of the DCCA cross-correlation coefficient, which contributes to acquiring more statistical characteristics of this measure. We resort to a synthetic time series that is followed by the integration and the detrending procedures of the DCCA cross-correlation coefficient, which divide the steps to estimate the coefficient into two portions. The former portion, including the integration and the detrending, is proved to be a linear transformation. The second portion is devoted to measuring Pearson’s $r$ between two synthetic time series. We confirm that the DCCA cross-correlation coefficient is also a linear measure by definition. The simulations including the ARFIMA processes and the multifractal binomial measures are numerically analyzed, which confirm the theoretical analysis.

The marginal ice zone (MIZ) around Antarctica is an important air–ice–ocean–wave interaction area and a crucial habitat for marine life. Given its dynamic nature, it is essential to understand and quantify both the short- and long-term changes of its extent. In this study, we investigated the MIZ extent time series using multifractal spectrum and $R$/$S$ analysis, examining Antarctica as a whole and per sub-region. The MIZ extent was predicted using a back-propagation (BP) algorithm. The results show that the wide multifractal spectrum width of the MIZ extent time series has strong multifractal features for the entire Antarctic and for the five sub-regions. By comparing the spectrum width of the original time series with those of a shuffled series, we found that multifractality is related to long-range correlations in the time series. The Hurst exponent obtained using the $R/S$ analysis indicates that the long-range correlation over six months is strongest for all time intervals. Compared to the autoregressive integrated moving average model, the mean absolute percentage error obtained using the BP algorithm was lower by 4–15%. We conclude that the BP algorithm combined with the multifractal property is well suited to predict the Antarctic MIZ extent.

Arterial blood pressure is modulated by several physiological regulatory processes. The analysis of beat-to-beat blood pressure dynamics provides information about cardiovascular control and patho-physiological conditions. In this paper we investigated the long-term correlations and fractal dimension of systolic blood pressure time series applying detrended fluctuation analysis (DFA) and Higuchi's algorithm (HFD). Thirty-minute blood pressure recordings in 25 patients with dilated cardiomyopathy (DCM) and 27 healthy controls (CON) were analyzed. The DFA and HFD revealed multifractal features in the blood pressure dynamics of CON as well as of DCM. At small scales, DFA and HFD of CON were significantly different from those of CON, reflecting patho-physiological changes. In conclusion, scaling analysis of blood pressure dynamics might lead to an enhanced assessment of autonomic cardiovascular control in patients with DCM.

This work describes the application of an important tool which can extract periodic information from the time-series of fluctuating traffic data. Compared to the traditional approach using FFT techniques, the nonlinear empirical mode decomposition (EMD) method has a number of advantages. This method is adaptive and therefore highly efficient at identifying embedded structures, even those with small amplitudes. Using this analysis, the traffic time series can be completely decomposed into five temporal modes including a 24-hour cycle, a 1-week cycle and a trend. Simultaneity, long-range correlations in traffic time series are investigated by detrended fluctuation analysis (DFA). In order to accurately capture the scaling exponents, EMD analysis is performed for DFA of the traffic records. The results of DFA for the data cleaned by subtracting the first intrinsic mode functions (IMF) are apparently improved, although the DFA curves are not entirely straight on the log-log plot.

This paper introduces a generalized diffusion entropy analysis method to analyze long-range correlation, then applies this method to stock volatility series, traffic congestion index and daily average temperature series of Beijing. The method uses the techniques of diffusion process and Rényi entropy to focus on the scaling behaviors of regular and extreme volatility of time series. However, crossovers arising from the extrinsic periodic trend make the scaling behavior difficult to analyze. Periodic trend is found to deeply affect correlation, as series present obscure scaling behavior while exhibiting obvious scaling behavior after the trend is removed. We introduce Fourier filtering method to eliminate the trend effects and systematically investigate the multifractal long-range correlation of traffic congestion index and daily average temperature series. For daily average temperature series of Beijing, regular volatility and extreme volatility both exhibit long-range persistence. For traffic congestion index series of Beijing, regular volatility exhibits un-correlation or short correlation, while extreme volatility reveals anti-persistence.

The present study calculates correlation energies of the different length poly(p-phenylenevinylene) (PPV) units using the formula recently developed for π conjugated polymers, and analyzes the correlation energies from the phenylene unit and the vinylene unit in single and three PPV unit cells as well as the effect of the correlation energies on the band energy gap of the PPV. The present method avoids the complicated numerical computations about the correlation effects for the π electronic conjugated molecule systems with large unit cells.

The characterization of long-range correlations and fractal properties of DNA sequences has proved to be a difficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengths with different nucleotide constitutions. In this paper we investigate statistical correlations among different positions in DNA sequences using the two-dimensional DNA walk. The root-mean-square fluctuation F(l) is described by a power law. The autocorrelation function C(l), which is used to measure the linear dependence and periodicity, exists a power law of C(l)-l^-μ. We also calculate the mean-square distance <R²(l)> along the DNA chain, and it may be expressed as <R²(l)>-l^r with 2>γ>1. Our investigations can provide some insights into long-range correlations in DNA sequences.

The objectives of this paper are to analyse the presence of multifractality in daily exchange rates of the US dollar (USD), British Pound (GBP), Euro (EUR), and Japanese Yen (JPY) relative to the Indian Rupee (INR) for a specific period (1999–2018) and to investigate the source of the observed multifractality in these exchange rates. The research examines the multifractal spectra of logarithmic returns (daily price changes) for the four currencies. To investigate the origins of this multifractality, we conduct two transformations on the return series: (a) random shuffling of the original time series of logarithmic returns which disrupts any long-range correlations within the data. And (b) application of phase randomisation on the unaltered series which aims to preserve frequency information while altering timing-related characteristics of the data. We then look at the impact of these transformations on the multifractality. Our findings indicate that all four exchange rates exhibit multifractal characteristics in their return series. The source of multifractality differs between currencies: The USD is primarily driven by the “fat tail” of the distribution (extreme fluctuations). For the GBP and EUR, a combination of long-range correlations and fat tails contributed to multifractality. The JPY is mainly influenced by the broad tail of the distribution (more frequent but smaller fluctuations). These results have implications for policymakers and market participants. Based on these findings, policymakers should consider the specific characteristics of each currency when designing risk management strategies or regulatory interventions.

The understanding of energy transfer mechanisms in a tokamak edge plasma is a major challenge for controlled fusion test reactors. High values of the Hurst exponent (H > 0.5) encountered in experimental probe data acquired in the scrape-off-layer (SOL) suggest the presence of long-range correlations favoring the hypothesis of an avalanche-type of radial transport. This communication aims at showing that this high value of Hurst coefficient does not necessarily imply the existence of long-time range correlations but it can be the witness of the presence of a particular behavior at small-time scales. Indeed, the development of a wavelet-based observer on synthetic signals, relying on fractional Brownian motions, has allowed the realization of a study model with mixed statistics. The associated time series, for which the H value is controlled, have been broken into blocks of variable length. Then, these different blocks have been scrambled randomly. Although potential long-range correlations have been thus destroyed, the wavelet-based estimator applied to these new synthetic signals is able to measure the original value of the Hurst parameter on a variable scale range. This approach highlights the persistence level on the scale range for several H and block size values. This technique reveals the reminiscent character of the synthetic process behavior appearing from small-time scales to long-time scales.