Diffusion Entropy Analysis Research Articles

Stock market stability: Diffusion entropy analysis

In this article, we propose a method to analyze the stock market stability based on diffusion entropy, and conduct an empirical analysis of Dow Jones Industrial Average. Empirical results show that this method can reflect the volatility and extreme cases of the stock market.

Multiscale multifractal diffusion entropy analysis of financial time series

This paper introduces a multiscale multifractal diffusion entropy analysis (MMDEA) method to analyze long-range correlation then applies this method to stock index series. The method combines the techniques of diffusion process and Rényi entropy to focus on the scaling behaviors of stock index series using a multiscale, which allows us to extend the description of stock index variability to include the dependence on the magnitude of the variability and time scale. Compared to multifractal diffusion entropy analysis, the MMDEA can show more details of scale properties and provide a reliable analysis. In this paper, we concentrate not only on the fact that the stock index series has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured. This time scale is related to the frequency band of the signal. We find that stock index variability appears to be far more complex than reported in the studies using a fixed time scale.

Multifractal diffusion entropy analysis: Optimal bin width of probability histograms

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi’s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal. We illustrate the utility of our approach by focusing on a scaling behavior of financial time series. In particular, we analyze the S&P500 stock index as sampled at a daily rate in the time period 1950–2013. In order to demonstrate a strength of the method proposed we compare the multifractal δ-spectrum for various bin-widths and show the robustness of the method, especially for large values of q. For such values, other methods in use, e.g., those based on moment estimation, tend to fail for heavy-tailed data or data with long correlations. Connection between the δ-spectrum and Rényi’s q parameter is also discussed and elucidated on a simple example of multiscale time series.

Fourier Filtering for Minimizing the Periodic Trend Effects on Multifractal Diffusion Entropy Analysis

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.

Multiscale Diffusion Entropy Analysis on Traffic Index Series

In this paper, we present a multiscale diffusion entropy analysis (DEA) for describing the traffic fractal dynamics with a spectrum of scale exponents . The method combines DEA with moving fitting window to analyze the traffic index (TI) series in different scales and shows more details of scale properties and provides a reliable analysis. We also quantify the effects of weather, traffic peaks on scale spectrum. The results indicate clearly that at large scales, the exponents show large volatility and they all have their own scale patterns. The multiscale DEA method provides new ways to measure the TI series and distinguishes groups in different conditions.

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

We are going back to the roots of the original solar neutrino problem: the analysis of data from solar neutrino experiments. The application of standard deviation analysis (SDA) and diffusion entropy analysis (DEA) to the Super-Kamiokande I and II data reveals that they represent a non-Gaussian signal. The Hurst exponent is different from the scaling exponent of the probability density function, and both the Hurst exponent and scaling exponent of the probability density function of the Super-Kamiokande data deviate considerably from the value of 0.5, which indicates that the statistics of the underlying phenomenon is anomalous. To develop a road to the possible interpretation of this finding, we utilize Mathai’s pathway model and consider fractional reaction and fractional diffusion as possible explanations of the non-Gaussian content of the Super-Kamiokande data.

On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided.

Comment on ‘multifractal diffusion entropy analysis on stock volatility in financial markets’ [Physica A 391 (2012) 5739–5745

In their recent article ‘multifractal diffusion entropy analysis on stock volatility in financial markets’ Huang, Shang and Zhao (2012) [6] suggested a generalization of the diffusion entropy analysis method with the main goal of being able to reveal scaling exponents for multifractal times series. The main idea seems to be replacing the Shannon entropy by the Rényi entropy, which is a one-parametric family of entropies. The authors claim that based on their method they are able to separate long range and short correlations of financial market multifractal time series. In this comment I show that the suggested new method does not bring much valuable information in obtaining the correct scaling for a multifractal/mono-fractal process beyond the original diffusion entropy analysis method. I also argue that the mathematical properties of the multifractal diffusion entropy analysis should be carefully explored to avoid possible numerical artefacts when implementing the method in analysis of real sequences of data.

Multifractal diffusion entropy analysis on stock volatility in financial markets

This paper introduces a generalized diffusion entropy analysis method to analyze long-range correlation then applies this method to stock volatility series. The method uses the techniques of the diffusion process and Rényi entropy to focus on the scaling behaviors of regular volatility and extreme volatility respectively in developed and emerging markets. It successfully distinguishes their differences where regular volatility exhibits long-range persistence while extreme volatility reveals anti-persistence.

Non-Ergodic to Ergodic Regime Transition via Intrusions in a Non-Poisson Renewal System with Power Law Tails

We study the effect of non-linear perturbations in the form of periodic intrusions in the case of a non-Poisson renewal system in the non-ergodic regime. We notice that, intrusions may cause the system to shift the power index and may even cause a transition from a non-ergodic regime to an ergodic regime. We have made the diffusion entropy analysis (DEA) of the system and notice that the change of the degree of complexity is consistent with the transition as well.

Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case

In this work, we analyse the long-run correlations of the seismic catalogue and of its clusters, by means of the Diffusion Entropy Analysis (DEA) and the value of the Hurst exponent. First we calculate the values for the whole catalogue, for the rate and the inter-event times and distance distribution over time, and subsequently we calculate the values for the declustered catalogue and the main clusters. We find a wide variety of behaviours, which depart from the Poisson statistics.

Lévy-like diffusion in eye movements during spoken-language comprehension

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

A study of the time distribution of inter-cluster earthquakes in Taiwan

In this study, we analyze the time distribution of inter-cluster earthquakes in Taiwan to infer correlation of earthquake occurrences. Our study based on the Diffusion Entropy Analysis (DEA) shows that there is positive correlation when the event time series is sampled by a time unit ranging from 120 to 1800 min. Also in the range of the time unit, two-slope feature in the determination of scaling exponent in DEA is observed, and the scenario is demonstrated by the simulations of synthetic earthquake sequence generated by the Copying Mistake Map model. Our simulation suggests that the earthquake sequence may consist of a randomness sequence and a correlated sequence, and the latter contributes to the correlation observed in our analysis.

Detrended fluctuation analysis in natural languages using non-corpus parametrization

The existence of long-range correlation in English and Korean had been reported by Montemurro et al. and Jaemi Bhan et al. This work extends this line of research to other languages (mainly Turkish), compares the differences between a meaningful text and a randomly created text by means of detrended fluctuation analysis and diffusion entropy analysis using a newly proposed parametrization which does not depend on corpus. The results imply a unique long-range correlation for each language analyzed, although similarities exist for languages of the same family.

Automated chirp detection with diffusion entropy: Application to infrasound from sprites

We study the performance of three different methods to automatically detect a chirp in background noise. (1) The standard deviation detector uses the computation of the signal to noise ratio. (2) The spectral covariance detector is based on the recognition of the chirp in the spectrogram. (3) The CASSANDRA detector uses diffusion entropy analysis to detect periodic patterns in noise. All three detectors are applied to an infrasound recording for detecting chirps produced by sprites. The CASSANDRA detector provides the best trade off between the false alarm rate and the detection efficiency.

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

The electricity market is a very peculiar market due to the large variety of phenomena thatcan affect the spot price. However, this market still shows many typical features ofother speculative (commodity) markets like, for instance, data clustering andmean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spotelectricity market (Nord Pool). We study the waiting time statistics betweenconsecutive spot price spikes and find it to show anomalous scaling characterizedby a decaying power law. The exponent observed in data follows a quite robustrelationship with the one implied by the DEA analysis. In terms of the DEA wealso revisit topics like clustering, mean-reversion and periodicities. We finallypropose a GARCH inspired model but for the price itself. Models in the context ofstochastic volatility processes appear under this scope to have a feasible description.

Comment on “Scaling Behavior of the Portevin–Le Chatelier Effect in an Al-2.5%Mg Alloy”

Recently Barat et al. [1] reported results of a scaling analysis using standard deviation (SD) and diffusion entropy(DE) analysis [2] of the stress-time series obtained from Al-Mg alloys deformed over a range of strain rates where the Portevin–Le Chatelier effect (PLC) is seen. The authors claim that the overall dynamics of the PLC effect follows a Levy-walk property in contrast with the chaotic or self-organized critical (SOC) dynamics reported earlier [3]. We show that this incorrect conclusion is an artifact of improper time series analysis. For constraints of space, we discuss results on SD analysis only.

SCALING BEHAVIOR AND COMPLEXITY OF THE PORTEVIN-LE CHATELIER EFFECT

The plastic deformation of dilute alloys is often accompanied by plastic instabilities due to dynamic strain aging and dislocation interaction. The repeated breakaway of dislocations from and their recapture by solute atoms leads to stress serrations and localized strain in the strain controlled tensile tests, known as the Portevin-Le Chatelier (PLC) effect. In this present work, we analyze the stress time series data of the observed PLC effect in the constant strain rate tensile tests on Al-2.5%Mg alloy for a wide range of strain rates at room temperature. The scaling behavior of the PLC effect was studied using two complementary scaling analysis methods: the finite variance scaling method and the diffusion entropy analysis. From these analyses we could establish that in the entire span of strain rates, PLC effect showed Levy walk property. Moreover, the multiscale entropy analysis is carried out on the stress time series data observed during the PLC effect to quantify the complexity of the distinct spatiotemporal dynamical regimes. It is shown that for the static type C band, the entropy is very low for all the scales compared to the hopping type B and the propagating type A bands. The results are interpreted considering the time and length scales relevant to the effect.

Diffusion entropy analysis on the scaling behavior of financial markets

In this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets. The scaling behaviors of four representative stock markets, Dow Jones Industrial Average, Standard&Poor 500, Heng Seng Index, and Shang Hai Stock Synthetic Index, are almost the same; with the scale-invariance exponents all in the interval [ 0.92 , 0.95 ] . We also estimate the local scaling exponents which indicate the financial time series is homogenous perfectly. In addition, a parsimonious percolation model for stock markets is proposed, of which the scaling behavior agrees with the real-life markets well.

Scaling Behavior of the Portevin–Le Chatelier Effect in anAl−2.5%MgAlloy

The scaling behavior of the Portevin-Le Chatelier (PLC) effect was studied by deforming an Al-2.5%Mg alloy for a wide range of strain rates. To reveal the exact scaling nature, the time series data of true stress versus time, obtained during deformation, were analyzed by two complementary methods: the finite variance scaling method and the diffusion entropy analysis. From these analyses we could establish that, in the entire span of strain rates, the PLC effect showed the Levy-walk property.