Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis

A method based on wavelet transform is developed to characterize variations at multiple scales in non-stationary time series. We consider two different financial time series, S&P CNX Nifty closing index of the National Stock Exchange (India) and Dow Jones industrial average closing values. These time series are chosen since they are known to comprise of stochastic fluctuations as well as cyclic variations at different scales. The wavelet transform isolates cyclic variations at higher scales when random fluctuations are averaged out; this corroborates correlated behaviour observed earlier in financial time series through random matrix studies. Analysis is carried out through Haar, Daubechies-4 and continuous Morlet wavelets for studying the character of fluctuations at different scales and show that cyclic variations emerge at intermediate time scales. It is found that Daubechies family of wavelets can be effectively used to capture cyclic variations since these are local in nature. To get an insight into the occurrence of cyclic variations, we then proceed to model these wavelet coefficients using genetic programming (GP) approach and using the standard embedding technique in the reconstructed phase space. It is found that the standard methods (GP as well as artificial neural networks) fail to model these variations because of poor convergence. A novel interpolation approach is developed that overcomes this difficulty. The dynamical model equations have, primarily, linear terms with additive Padé-type terms. It is seen that the emergence of cyclic variations is due to an interplay of a few important terms in the model. Very interestingly GP model captures smooth variations as well as bursty behaviour quite nicely.      

Cumulative Clearness Index Frequency Distributions on the Territory of the Russian Federation

Cumulative distributions of clearness index values are constructed for the territory of Russia based on ground observation results and NASA POWER data. The obtained distributions lie close to each other, which means that the NASA POWER data can be used in solar power installations simulation at temperate and high latitudes. Approximation of the obtained distributions is carried out. The values of equation coefficients for the cumulative clearness index distributions constructed for a wide range of climatic conditions are determined. Equations proposed for a tropical climate are used in the calculations, so they can be regarded as universal ones.     

Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined.A basic one-factor model is then proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a ‘market plus sectors’ model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data. By partitioning the eigenvalue time series, we then show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. The study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies.     

Asset returns and volatility clustering in financial time series

An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial time series. We also introduce an index to quantitatively measure the clustering behaviour of fluctuations in these time series and show that big losses in financial markets usually lump more severely than big gains. We further give examples to demonstrate that comparing to conventional methods, our index enables one to extract more information from the financial time series.     

Frequency-dependent conductivity in ionic glasses: A possible model

The frequency-dependent (ac) conductivity behaviour of ionically conducting glasses is discussed. A critique is given of the treatment of Almond and West for this behaviour. Two models are proposed instead to account for the observed ac loss data. One involves parallel relaxation processes and is a modification of a model originally developed for the case of large-polaron transport in amorphous semiconductors. The other is based on series relaxation, and is based on a model originally proposed by Glarum for the case of dielectric relaxation in molecular liquids. In the development given here, this model is modified so as to describe ionic transport, and a new microscopic transport mechanism is proposed—“diffusion-controlled relaxation”—which satisfies the requirements of the Glarum theory and which naturally incorporates cooperative ionic motions. For this reason, it is intuitively more appealing.     

Event Based Interpretation of Schr?dinger’s Equation for the Two-slit Experiment

A discrete time event based model is constructed for particles emitted one-at-a-time in the two slit experiment of quantum mechanics. It is shown that the simulations of the model align with the solutions of the time-dependent non-relativistic Schr?dinger’s equation corresponding to the experiment. The event based model provides an interpretation of the two slit experiment as the aggregate behaviour of individual particles, whose paths are probabilistically differentiated according to sequential rules for their discrete spatial movements in time.     

Scaling in the bombay stock exchange index

In this paper we study Bombay stock exchange (BSE) index financial time series for fractal and multifractal behaviour. We show that BSE index time series is monofractal and can be represented by a fractional Brownian motion.     

The emergence of coordination in public good games

In physical models it is well understood that the aggregate behaviour of a system is not in one to one correspondence with the behaviour of the average individual element of that system. Yet, in many economic models the behaviour of aggregates is thought of as corresponding to that of an individual. A typical example is that of public goods experiments. A systematic feature of such experiments is that, with repetition, people contribute less to public goods. A typical explanation is that people “learn to play Nash” or something approaching it. To justify such an explanation, an individual learning model is tested on average or aggregate data. In this paper we will examine this idea by analysing average and individual behaviour in a series of public goods experiments. We analyse data from a series of games of contributions to public goods and as is usual, we test a learning model on the average data. We then look at individual data, examine the changes that this produces and see if some general model such as the EWA (Expected Weighted Attraction) with varying parameters can account for individual behaviour. We find that once we disaggregate data such models have poor explanatory power. Groups do not learn as supposed, their behaviour differs markedly from one group to another, and the behaviour of the individuals who make up the groups also varies within groups. The decline in aggregate contributions cannot be explained by resorting to a uniform model of individual behaviour. However, the Nash equilibrium of such a game is a total payment for all the individuals and there is some convergence of the group in this respect. Yet the individual contributions do not converge. How the individuals “self-organsise” to coordinate, even in this limited way remains to be explained.     

A new approach to determining the waveguide mode index distribution

A new approach is presented to determining the profile characteristics of planar optical waveguides. The mode index value is developed into the Lagrange series in terms of mode number, which allows one to find analytical expressions for the coefficients of that series. This method is applied to evaluating the coefficients of mode index distribution for the step-index and four-layer step-index profiles.     

About the Morin transition in hematite in relation with particle size and aluminium substitution

The results of a M?ssbauer study of the Morin transition behaviour in three series of hematite and Al-hematite samples are reviewed and discussed. The first two series comprise small-particle hematites and Al-hematites prepared from decomposition of lepidocrocite, whereas in the third series Al-hematites up to the μm range are obtained from co-precipitated oxinates. It is demonstrated that the Morin transition temperature follows quite well the overall properties of the samples such as particle size and Al substitution, while the transition region is rather determined by all kind of distributive effects. A model involving intermediate states is suggested for the Morin transition behaviour in non-ideal hematite. Presented at the International Colloquium “M?ssbauer Spectroscopy in Materials Science”, Velké Losiny, Czech Republic, 3–8 September 2000. Finacial support from the FWO-Flanders (project G.000797) and the Belgian Federal Interuniversity Attraction Pole (PAI/UIAP) on reduced dimensionalities is acknowledged.     

Non-sequential effects in the decay of resonant states

Fano and Prats' treatment of continuum-continuum interaction is used to study the time-dependent behaviour of a system initially in a discrete state coupled to a continuum which is itself coupled to another continuum. This level scheme represents a limiting case in a model which is currently used in the theory of molecular processes, the opposite limit being the sequential scheme which leads to chain-like rate equations. A very different behaviour is obtained in the two limits. In contrast with the results of the sequential model the continuum-continuum coupling produces a change (a decrease) in the decay rate of the discrete state. The two continua are populated in parallel. The calculations provide an explicit example of the influence of higher order terms on a rate constant, a problem which has received attention recently in relation to the evaluation of non-radiative transition rates using approximate molecular wave functions.     

Generalized clearness index frequency curves for the Russian Federation

Actinometric data of World Radiation Data Center and NASA POWER were used to get daily clearness index frequencies for Russia. The results obtained provide the opportunity to estimate more accurately the output of various types of solar power plants. Frequencies determined using the data sources indicated correlate well and differ from universal dependences that were recommended earlier for the entire globe.     

Interaction between two active structural paths for source mass motion control over mid-frequency range

The interaction between two active structural paths is analytically and experimentally studied as part of a resonating source-path-receiver system, where each path consists of a piezoelectric stack actuator in series with an elastomeric (passive) mount. An analytical model of the system is first developed, and then an experiment is constructed to verify the feasibility. Good agreement is found between the model and experiment. A performance index to characterize the active path interaction for source mass motion control up to 1000 Hz is analytically defined; it considers the passive phase interaction (caused by system dynamics) between the active mounts and the resulting system motion. Two passive system parameters (rubber path structural damping and disturbance moment arm) emerge as key design variables that drastically change the performance index, and guidelines are developed for desirable path interactions. Limited experimental validation demonstrates that active source mass motion control is achieved at 400 Hz using piezoelectric stack actuators.     

Discovery,characterization and modelling of novel shape memory behaviour of fcc metal nanowires

Novel shape memory behaviour was discovered recently in single-crystalline fcc nanowires of Cu, Ni and Au with lateral dimensions below 5?nm. Under proper thermomechanical conditions, these wires can recover elongations up to 50%. This phenomenon only exists at the nanoscale and is associated with reversible lattice reorientations within the fcc lattice structure driven by surface stresses. Whereas the propagation of partial dislocations and twin planes specific to fcc metals are the required mechanism, only materials with higher propensities for twinning (e.g. Cu and Ni) show this behaviour and those with lower propensities for twinning (e.g. Al) do not. This paper provides an overview of this novel behaviour with a focus on the transformation mechanism, driving force, reversible strain, size and temperature effects and energy dissipation. A mechanism-based micromechanical continuum model for the tensile behaviour is developed. This model uses a decomposition of the lattice reorientation process into a reversible, smooth transition between a series of phase-equilibrium states and a superimposed irreversible, dissipative propagation of a twin boundary. The reversible part is associated with strain energy functions with multiple local minima and quantifies the energy conversion process between the twinning phases. The irreversible part is due to the ruggedness of the strain energy landscape, associated with dislocation nucleation, gliding and annihilation, and characterizes the dissipation during the transformation. This model captures all major characteristics of the behaviour, quantifies the size and temperature effects and yields results which are in excellent agreement with data from molecular dynamics simulations.     

Series resonance circuit with ferroelectric capacitor

A series resonance circuit under sinuousoidal driving is investigated experimentally. The inductance consists of an air coil. The capacitance is made up of a ferroelectric material that introduces its nonlinear dielectric properties into the circuit. The dynamical system linear coil-nonlinear capacaitor shows an interesting behaviour. The phase portrait differs in general from the ellipse of the harmonic oscillator. For appropriate external conditions period doubling sequences, chaos and therein enclosed periodic windows might occur. Starting from a cubic nonlinearity of the dielectric properties a Duffing equation is proposed as a model for periodic behaviour of the series resonance circuit. Simulations of experimentally recorded phase portraits yield good agreement between experiment and model.     

Hierarchical centralities of information transmissions in reaching a consensus

The question, how central indications arise from an undirected environment and lead to collective behaviors, is analyzed based on a simple model of opinion dynamics, called the DeGroot model. We first reformulate the necessary and sufficient condition for reaching a consensus, then the condition is used to set up the pattern of information transmissions. By classifying the individuals into a sequential series of classes and by giving the dynamic contents of centrality, we demonstrate that the hierarchical centralities with descend strength are associated with the sequential series of classes in information transmissions. The results provide wide applications in social engineering, an example about the merger of different groups is discussed.     

混合交通流时间序列的去趋势波动分析

应用去趋势波动分析法研究交通流时间序列的复杂性,探讨了混合交通流时间序列演变行为的标度指数.根据标度指数的变化特征,进而揭示交通流时间序列所具有的长程相关性和短程相关性.通过分析发现,存在一密度ρ,当ρ₁<ρ<ρ₂时,交通流时间序列具有长程相关性;而当ρ<ρ₁或ρ>ρ₂时,交通流时间序列具有短程相关性,即密度的变化影响着标度指数的变化.另外分析了在不同慢车比率条件下时间序列的标度指数,发现慢车比率的变化 关键词： 混合交通流 去趋势波动分析 时间序列 长程相关     

Neutron thresholds to resonant analogue states

The anomalous energy behaviour of the neutron threshold to a resonant analogue state is investigated in detail. The analysis is applied to recently studied reactions of the type A(d, np)A but can equally well be applied to reactions involving other projectiles. To avoid all three-body effects, the reaction is assumed to be a sequential process, i.e. the resonant intermediate analogue state has a finite lifetime. An expression for the energy behaviour at threshold is obtained.     

Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach

The aim of this study is to assess and compare changes in regularity in the 36 European and the U.S. stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021. The proposed research hypothesis states that entropy of an equity market index decreases during turbulence periods, which implies that regularity and predictability of a stock market index returns increase in such cases. To capture sequential regularity in daily time series of stock market indices, the Sample Entropy algorithm (SampEn) is used. Changes in the SampEn values before and during the particular turbulence period are estimated. The empirical findings are unambiguous and confirm no reason to reject the research hypothesis. Moreover, additional formal statistical analyses indicate that the SampEn results are similar both for developed and emerging European economies. Furthermore, the rolling-window procedure is utilized to assess the evolution of SampEn over time.     

Multifractal detrended fluctuation analysis of the Chinese stock index futures market

Based on the multifractal detrended fluctuation analysis (MF-DFA) and multifractal spectrum analysis, this paper empirically studies the multifractal properties of the Chinese stock index futures market. Using a total of 2942 ten-minute closing prices, we find that the Chinese stock index futures returns exhibit long-range correlations and multifractality, making the single-scale index insufficient to describe the futures price fluctuations. Further, by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure, we show the existence of two different sources of the multifractality for the Chinese stock index futures market. Our results suggest that the multifractality is mainly due to long-range correlations, although the fat-tailed probability distributions also contribute to such multifractal behaviour.