Recurrence quantification analysis of global stock markets

This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures.     

Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes

Recurrence Plots are graphical tools based on Phase Space Reconstruction. Recurrence Quantification Analysis (RQA) is a statistical quantification of RPs. RP and RQA are good at working with non-stationarity and noisy data, in detecting changes in data behavior, in particular in detecting breaks, like a phase transition and in informing about other dynamic properties of a time series. Endogenous Stock Market Crashes have been modeled as phase changes in recent times. Motivated by this, we have used RP and RQA techniques for detecting critical regimes preceding an endogenous crash seen as a phase transition and hence give an estimation of the initial bubble time. We have used a new method for computing RQA measures with confidence intervals. We have also used the techniques on a known exogenous crash to see if the RP reveals a different story or not. The analysis is made on Nifty, Hong Kong AOI and Dow Jones Industrial Average, taken over a time span of about 3 years for the endogenous crashes. Then the RPs of all time series have been observed, compared and discussed. All the time series have been first transformed into the classical momentum divided by the maximum Xmax of the time series over the time window which is considered in the specific analysis. RPs have been plotted for each time series, and RQA variables have been computed on different epochs. Our studies reveal that, in the case of an endogenous crash, we have been able to identify the bubble, while in the case of exogenous crashes the plots do not show any such pattern, thus helping us in identifying such crashes.     

Measuring volatility in the Nordic spot electricity market using Recurrence Quantification Analysis

In this work, we have applied Recurrence Quantification Analysis (RQA)to data sets taken from the Nordic spot electricity market. Our main interest was in trying to correlate their volatility with variables obtained from the quantification of recurrence plots (RP). For this reason we have based our analysis on known historical events: the evolution of the Nord Pool market and climatic factors, i.e. dry and wet years, and we have compared several dispersion measures with RQA measures in correspondence of these events. The analysis suggests that two RQA measures: DET and LAM can be used as a measure of the inverse of the volatility. The main advantage of using DET and LAM is that these measures provide also information about the underlying dynamics. This fact is shown using shuffled and linear Gaussian surrogates of the real time series.     

Selection of recurrence threshold for signal detection

Over the last years recurrence plots (RPs)and recurrence quantification analysis (RQA)have become quite popular in various branches of science. One key problem in applying RPs and RQA is the selection of suitable parameters for the data under investigation. Whereas various well-established methods for the selection of embedding parameters exists, the question of choosing an appropriate threshold has not yet been answered satisfactorily. The recommendations found in the literature are rather rules of thumb than actual guidelines. In this paper we address the issue of threshold selection in RP/RQA. The core criterion for choosing a threshold is the power in signal detection that threshold yields. We will validate our approach by applying it to model as well as real-life data.     

Effectiveness of Recurrence Quantification Measures in Discriminating Subjects With and Without Voice Disorders

The objective of this study was to analyze the accuracy of recurrence quantification measurements (RQMs) in discriminating between individuals with and without voice disorders. This study consisted of a total of 541 recorded voice samples from normal and dysphonic subjects. All subjects recorded a sustained vowel /Ɛ/ and underwent a laryngoscopic examination of the larynx. Twelve RQMs and three parameters related to the topology of the phonatory system were extracted from the samples, for a total of 15 measures. The classification used quadratic discriminant analysis and includes the measures of accuracy, sensitivity, and specificity. Single measurements such as Shannon's entropy, average diagonal length, and transitivity had only acceptable performance ratings (≥70%) in discriminating between individuals with and without voice disorders. The combination of the parameters average diagonal length, Shannon's entropy, trapping time, length of the longest vertical line, tau, imbedding dimension, neighborhood radius, and transitivity produced the highest accuracy in discrimination (83.27%). Therefore, the performance of RQMs related to the formation of diagonal lines in classifying individuals with and without voice disorders was acceptable at ≥70%. A combination of RQMs showed good performance in discriminating between the study groups, with higher sensitivity and specificity.     

Comment on “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” by Rohde et al. [Physica D 237 (2008) 619-629]

In the recent article “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.Nevertheless, we also clearly assert that an uncritical application of RQA may lead to wrong conclusions.     

Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.     

Confidence bounds of recurrence-based complexity measures

In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real-life data.     

Recurrence analysis of the Portevin-Le Chatelier effect

Tensile tests were carried out by deforming polycrystalline samples of Al-2.5%Mg alloy at room temperature in a wide range of strain rates where the Portevin-Le Chatelier (PLC) effect was observed. The experimental stress-time series data have been analyzed using the recurrence analysis technique based on the Recurrence Plot (RP) and the Recurrence Quantification Analysis (RQA) to study the change in the dynamical behavior of the PLC effect with the imposed strain rate. Our study revealed that the RQA is able to detect the unique crossover phenomenon in the PLC dynamics.     

The microscopic investigation of structures of moving flux lines by neutron and muon techniques

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T _c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Detection of the fracture zone by the method of recurrence plot

Recurrence plots (RPs) and recurrence quantification analysis (RQA) characteristics for the normal component of the displacement vector upon excitation of a defect steel plate by a sound pulse are analyzed. Different cases of spatial distribution of defects (uniform and normal) are considered, and a difference in the RQA parameters in these cases is revealed.     

Influences of flexible defect on the interplay of supercoiling and knotting of circular DNA

Knots are discovered in biophysical systems, such as DNA and proteins. Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending angle resulting in flexible defects. The role of flexible defects in the interplay of supercoiling and knotting of circular DNA were predicted by a Monte Carlo simulation. In knotted DNA with a particular knot type, a flexible defect noticeably enhances the supercoiling of the knotted DNA and the decreasing excitation energy makes the knotted portion more compact. A reduction in twist rigidity and unwinding of flexible defects are incorporated into the numerical simulations, so that interplay of supercoiling and knotting of circular DNA is studied under torsional conditions. Increasing unwinding not only results in a wider linking number distribution, but also leads to a drift of the distribution to lower values. A flexible defect has obvious effects on knotting probability. The summation of equilibrium distribution probability for nontrivial knotted DNA with different contour length does not change with excitation energy monotonically and has a maximum at an intermediate value of excitation energy around 5 kBT. In the phase space of knot length and gyration radius of knotted DNA, knot length does not anticorrelate with its gyration radius, which is attributed to the flexible defect in the knotted portion, which leads to the release of bending energy and inhibited the competition between entropy and bending energy.     

Fluid molecule oscillations and the continuous spectrum near the rayleigh line

Of late there have been considerable developments in the theoretical study of the contour of spectral lines and the Rayleigh line by general statistical methods in the theory of random processes. On the basis of the general equations describing the rotational motion of molecules [1,2], and also of the equation which describes the change in the projection of the dipole moment onto the laboratory coordinate axes [3], we seek a correlation function whose Fourier transform leads finally to the required spectral distribution. In the present article we solve the problem of the spectral distribution by a direct analysis of the change in the projection onto the laboratory coordinate axes of the dipole moment induced in a molecule by an incident light wave. We consider a specific model for the rotational motion of fluid molecules.     

Entropy of isolated quantum systems after a quench

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.     

Estimating Phase Amplitude Coupling between Neural Oscillations Based on Permutation and Entropy

Cross-frequency phase–amplitude coupling (PAC) plays an important role in neuronal oscillations network, reflecting the interaction between the phase of low-frequency oscillation (LFO) and amplitude of the high-frequency oscillations (HFO). Thus, we applied four methods based on permutation analysis to measure PAC, including multiscale permutation mutual information (MPMI), permutation conditional mutual information (PCMI), symbolic joint entropy (SJE), and weighted-permutation mutual information (WPMI). To verify the ability of these four algorithms, a performance test including the effects of coupling strength, signal-to-noise ratios (SNRs), and data length was evaluated by using simulation data. It was shown that the performance of SJE was similar to that of other approaches when measuring PAC strength, but the computational efficiency of SJE was the highest among all these four methods. Moreover, SJE can also accurately identify the PAC frequency range under the interference of spike noise. All in all, the results demonstrate that SJE is better for evaluating PAC between neural oscillations.     

Localization and level statistics in a one-dimensional solid state model with periodically modulated potential

For a solid state model described by a band matrix with diagonal elements depending periodically on the siteindex we determine the eigenstates and their localization length. The periodicity of the diagonal elements gives rise to the appearance of a pronounced peak structure of the eigenstates with the same period. The same type of peak-structure is present in the quasi-energy states of some periodically driven quantum systems, and can be associated with a nearly conversed quasi-momentum quantum number. We investigate the influence of the periodic peak structure on the nearest neighbor level spacing distribution and find that the nearly conserved quasi-momentum modifies but does not destroy the level repulsion expected for a Gaussian orthogonal ensemble.     

Frictional shakedown and ratcheting of an oscillating cylindrical,elastic contact with coulomb friction

We examine frictional shakedown of an elastic contact of a cylinder pressed on a flat substrate. Slight oscillatory rolling of the cylinder varies the pressure distribution and the contact region. Together with the tangential load, this rocking motion causes incremental sliding processes and a macroscopic rigid body motion. In case that the oscillation amplitude is sufficiently small, the slip ceases after the first few periods and a safe shakedown occurs: the residual force in the contact withstands the tangential load. Otherwise ratcheting occurs: one side of the contact alternately sticks, while the other slips. This leads to a continuing rigid body motion. By derivation of the tangential stress distribution and use of the Boussinesq and Cerruti potential functions, we find approximations for the shakedown limits for the tangential load and the oscillation amplitude. This allows the accurate prediction of the displacement and the reduced tangential load capacity in the shakedown state. The results show strong agreement with numerical and experimental data.     

Recurrence analysis and synchronization of oscillators with coexisting attractors

The method of recurrence plots (RPs) has been traditionally used for experimental time series analysis with no comparison with the mathematical model. This is in part because of lack of nonlinear analysis of mathematical model based on the recurrence quantification analysis (RQA) parameters. The paper provides substantial information about the mathematical and numerical analysis and synchronization of a multi-limit cycle oscillator from the RQA perspective. The recurrence quantification analysis parameters are used to discuss the birhythmic behavior of the system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response. Finally, the results of the method of RPs are compared to those of phase diagrams and the problem of synchronization of limit cycle and chaotic response is discussed by the mean of cross recurrence.