Stochastic Properties Research Articles

Biclustering high‐frequency financial time series based on information theory

AbstractClustering a large number of time series into relatively homogeneous groups is a well‐studied unsupervised learning technique that has been widely used for grouping financial instruments (say, stocks) based on their stochastic properties across the entire time period under consideration. However, clustering algorithms ignore the notion of biclustering, that is, grouping of stocks only within a subset of times rather than over the entire time period. Biclustering algorithms enable grouping of stocks and times simultaneously, and thus facilitate improved pattern extraction for informed trading strategies. While biclustering methods may be employed for grouping low‐frequency (daily) financial data, their use with high‐frequency financial time series of intra‐day trading data is especially useful. This paper develops a biclustering algorithm based on pairwise or groupwise mutual information between one‐minute averaged stock returns within a trading day, using jackknife estimation of mutual information (JMI). We construct a multiple day time series biclustering (MI‐MDTSB) algorithm that can capture refined and local comovement patterns between groups of stocks over a subset of continuous time points. Extensive numerical studies based on high‐frequency returns data reveal interesting intra‐day patterns among different asset groups and sectors.

Memory propagation in barrier discharge at water interface: suspected Markov states and spatiotemporal memory effects

Barrier discharges are known for strong memory effects which shape their stochastic properties. We study memory propagation in a surface barrier discharge operated at the water interface in atmospheric pressure air using electrical measurements and synchronized intensified CCD imaging. Comprehensive electrical data sets of seemingly chaotic behaviour are evaluated from thousands of subsequent periods recorded with high temporal resolution and large dynamic range. We confirm known memory effects and identify new ones both in between the half-periods as well as between subsequent pulses within one half-period. We find two memoryless states for the first discharges in the positive polarity which are defined by the presence/absence of photoemission-induced collective behaviour. Given the determined probability for entering one of these two suspected Markov states, the system bifurcates and follows one of the two subsequent non-Markovian pathways. The identification of the collective behaviour in these pathways enables us to recognize the spatially resolved property of the system and to determine its probability of occurrence, both solely from the zero-dimensional electrical characterisation.

Probabilistic failure analysis of quasi-isotropic CFRP structures utilizing the stochastic finite element and the Karhunen–Loève expansion methods

The accuracy of structural analysis in composite structures depends on the proper estimation of the uncertainties mainly related to the mechanical properties of the constituent materials. On this basis, a sophisticated numerical tool is proposed, able to perform stochastic finite element analysis on composite structures with material uncertainties by distributing stochastic mechanical properties along the domain of a composite structure. The output of the analysis is a probability density function for the deformation, strain, stress and failure fields. The proposed tool exploits the Karhunen–Loève expansion and the Latin Hypercube Sampling methods for the stochastic distribution of the mechanical properties, the well-established First-Order Shear Deformation theory in conjunction with a random variable approach for the calculation of stochastic stiffness matrices, and the Puck’s failure criterion for the conduction of probabilistic analysis of different failure modes in composite structures. A quasi-static tensile testing campaign was conducted with quasi-isotropic coupons in order to assess the fidelity of the method and the efficiency of the stochastic distribution algorithm is compared with the full field data acquired by the digital image correlation approach. The current paper provides a thorough presentation of the development of the proposed stochastic finite element method and validation results which ensure the efficiency of the proposed stochastic numerical tool. • The Karhunen–Loève expansion is utilized for efficient random distribution of mechanical properties. • The Latin Hypercube Sampling is utilized for randomness generation and it outperforms the Monte Carlo Simulation. • Stochastic finite elements are developed for probabilistic failure analysis using Puck’s failure criterion. • Digital image correlation data are obtained from tensile experiments to assess the inherent randomness of composites.

Statistical Model Checking for Stochastic and Hybrid Autonomous Driving Based on Spatio-Clock Constraints

Autonomous driving vehicles are a kind of typical cyber-physical systems integrating complex interactions between hardware and software components such as collaborative computation, distributed communication, and spatio-clock synchronous control with surrounding traffic environment. They can percept the environment, communicate with surroundings, and react fast enough to control independently. The purpose of autonomous driving emergence is to improve driving safety, reduce environmental pollution, and ease the traffic congestion. However, new features with surrounding open and dynamic environment make systems design and verification becoming more and more complex than ever, such as stochastic communication delay, hardware spontaneous failure distribution, and natively hybrid behaviors described by ordinary differential equations. Spatial and time collision avoidance remains crucial obstacles on the path to becoming ubiquitous and dependable. In this paper, we adopt statistical model checking (SMC) to enlighten possible hazards affected by stochastic and hybrid features in the design phase of autonomous driving systems. In order to provide safety and accountability, we first propose a dedicated multi-lane spatio-clock stochastic specification language (MLSCL) to describe safety invariants and guards in domain-specific autonomous driving systems. Then, we present the semantic mapping rules between MLSCL and UPPAAL SMC models, and design the spatio-clock stochastic and hybrid automata based on MLSCL in order to model inherently stochastic and hybrid behaviors. Finally, we present an illustrative lane-change case study to verify spatio-clock stochastic and hybrid-related properties adopting SMC, and demonstrate the effectiveness of our proposed approach.

An innovative method of fault detection in power transformers

The Bayesian classifier is a priori the optimal solution for minimizing the total error in problems of statistical pattern recognition. The article suggests using the classifier as a regular tool to increase the reliability of defect recognition in power oil-filled transformers based on the results of the analysis of gases dissolved in oil. The wide application of the Bayesian method for solving tasks of technical diagnostics of electrical equipment is limited by the problem of the multidimensional distribution of random parameters (features) and the nonlinearity of classification. The application of a generalized feature of a defect in the form of a nonlinear function of the transformer state parameters is proposed. This simultaneously reduces the dimension of the initial space of the controlled parameters and significantly improves the stochastic properties of the random distribution of the generalized feature. A special algorithm has been developed to perform statistical calculations and the procedure for recognizing the current technical condition of the transformer using the generated decision rule. The presented research results illustrate the possibility of the practical application of the developed method in the conditions of real operation of power transformers.

An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations

An epidemic model with the saturated incidence rate and the environmental fluctuations is investigated in this paper. We study the extinction and the persistence in the mean, and stationary distribution of the solution as well. By contradiction, we firstly show that stochastic epidemic model admits a unique global positive solution for any given positive initial value. Further, when R˜0>1 is valid, we derive the persistence in the mean, and also prove the existence of an ergodic stationary distribution by constructing moderate functions. By comparison theorem of stochastic differential equations and properties of inequalities, the extinction of the solution is finally derived when R0<1 and ν<0 hold, where ν indicates the exponential rate for decline. Meanwhile, the distribution for the density of the susceptible is estimated. As a consequence, numerical simulations and illustrative examples are separately carried out to support the main results of this paper.

Variational Bayesian approximation based robust adaptive single beacon navigation method

For the practical application of single beacon navigation system, effective sound velocity (ESV) setting error, measurement outliers and unknown noise statistical parameters are the major sources of positioning error. Although the unknown ESV of single beacon navigation system has been well studied, the other two sources are less concerned. The performance of existing state-of-art navigation methods will deteriorate when there are measurement outliers or noise statistical parameters setting error. This paper aims to fill the gap. We model the process and measurement noise of each state and measurement component based on their own stochastic properties, so that, the influence of measurement outliers can be incorporated into stochastic model. The unknown noise statistical parameters are regarded as random variables and the variational Bayesian approximation method is used to estimate them along with the navigation state. The corresponding robust adaptive single beacon navigation method is proposed. Moreover, the simulation and field data demonstrate that the proposed method is superior to the existing state-of-art navigation methods in the presence of measurement outliers and unknown noise statistical parameters.

Hysteresis and stochastic convergence in Eurozone unemployment rates: evidence from panel unit roots with smooth breaks and asymmetric dynamics

Research background: Studying the dynamic characteristics of unemployment rate is crucial for both economic theory and macroeconomic policies. Despite numerous research, the empirical evidence about stochastic behaviour of the unemployment rate remains disputable. It has been widely agreed that most economic variables, including unemployment rates, are characterized by both structural breaks and nonlinearities. However, a little work is done to examine both features simultaneously. Purpose of the article: In this paper, we analyse the stationarity properties of unemployment rates of Euro area member countries. Also, we aim to test stochastic convergence of unemployment rates among member countries. Our empirical procedures explicitly allow for simultaneous gradual breaks and nonlinearities in the series. Methods: This paper develops a new unit root test procedure for panel data, allowing for both gradual structural breaks and asymmetric adjustment towards equilibrium. We carry out Monte Carlo simulations to examine small sample performance of the proposed test procedure and compare it to the existing test procedures. We apply the newly proposed test to examine the stochastic properties of the unemployment rates of Euro-member countries as well as relative unemployment rates vis-?-vis the Eurozone unemployment rate. Findings &amp; value added: We find that the newly developed test procedure outperforms existing tests in highly nonlinear settings. Also, these tests reject the null hypothesis of unit root in more cases when compared to the existing tests. We find stationarity in the series only after allowing for structural breaks in the data generating process. Allowing for nonlinear and asymmetric adjustment in addition to gradual breaks provides evidence of stationarity in more cases. Furthermore, our results suggest that relative unemployment rate series are stationary, providing evidence in favour of stochastic convergence in unemployment rates. Overall, our results imply a limited room for coordinated economic policy to fight unemployment in the Eurozone.

Probing Diffusive Dynamics of Natural Tubule Nanoclays with Machine Learning

Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically important properties is natural and cannot be artificially reproduced one-to-one in the laboratory? The situation becomes even more complicated when we are interested in exploring stochastic properties of a natural system and only a limited set of noisy experimental data is available. In this paper we address these problems by exploring diffusive motion of some natural clays, halloysite and sepiolite, in a liquid environment. By using a combination of dark-field microscopy and machine learning algorithms, a quantitative theoretical characterization of the nanotubes' rotational diffusive dynamics is performed. Scanning the experimental video with the gradient boosting tree method, we can trace time dependence of the diffusion coefficient and probe different regimes of nonequilibrium rotational dynamics that are due to contacts with surfaces and other experimental imperfections. The method we propose is of general nature and can be applied to explore diffusive dynamics of various biological systems in real time.

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

AbstractIn reliability engineering literature, a large number of research papers on optimal preventive maintenance (PM) of technical systems (networks) have appeared based on preliminary many different approaches. According to the existing literature on PM strategies, the authors have considered two scenarios for the component failures of the system. The first scenario assumes that the components of the system fail due to aging, while the second scenario assumes the system fails according to the fatal shocks arriving at the system from external or internal sources. This article reviews different approaches on the optimal strategies proposed in the literature on the optimal maintenance of multi‐component coherent systems. The emphasis of the article is on PM models given in the literature whose optimization criteria (cost function and stationary availability) are developed by using the signature‐based (survival signature‐based) reliability of the system lifetime. The notions of signature and survival signature, defined for systems consisting of one type or multiple types of components, respectively, are powerful tools assessing the reliability and stochastic properties of coherent systems. After giving an overview of the research works on age‐based PM models of one‐unit systems and ‐out‐of‐ systems, we provide a more detailed review of recent results on the signature‐based and survival signature‐based PM models of complex systems. In order to illustrate the theoretical results on different proposed PM models, we examine two real examples of coherent systems both numerically and graphically.

Market efficiency in non-renewable resource markets: evidence from stationarity tests with structural changes

The dynamics of metal prices are highly significant for worldwide economic activity due to metals being key intermediate inputs to industrial production and construction and treated as investment assets. In that sense, this study investigates the efficient market hypothesis, i.e., predictability of price patterns, for several non-renewable resources, namely copper, lead, tin, nickel, zinc, aluminum, gold, platinum, and silver. Our period covers 1980Q1–2019Q4, during which metal markets witnessed many extraordinary times due to market-specific and global factors. Accounting for the importance of the potential breaks in the analysis of stochastic properties of non-renewable resource prices, we utilize two different stationarity tests; one is designed to capture smooth breaks, and the other one is designed to detect abrupt changes in the prices. Our empirical results reveal that none of the prices, except silver, can be characterized by the efficient market hypothesis. They follow stationary and predictable patterns with structural changes related to market-specific and global economic events, though concerns on economic uncertainties appeared to be more effective on precious metals.

The conditional spacings and their stochastic properties

In this paper, the concepts of conditional spacings and normalized conditional ones are introduced when a series system with independent and identically distributed components fails at time t. First the marginal survival function and joint survival function of conditional spacings are obtained. And some stochastic comparisons between different spacings are conducted. Moreover, the case when the component lifetimes are independent and distributed as Exponential is investigated. And some statistical properties of conditional spacings are naturally given. In the end, the dependence for the conditional spacings is investigated.

Stochastic evolutionary stability in matrix games with random payoffs.

Evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behavior, but also widely used in economics and social sciences. Recently, in order to reveal the stochastic dynamical properties of evolutionary games in randomly fluctuating environments, the concept of stochastic evolutionary stability based on conditions for stochastic local stability for a fixation state was developed in the context of a symmetric matrix game with two phenotypes and random payoffs in pairwise interactions [Zheng et al., Phys. Rev. E 96, 032414 (2017)2470-004510.1103/PhysRevE.96.032414]. In this paper, we extend this study to more general situations, namely, multiphenotype symmetric as well as asymmetric matrix games with random payoffs. Conditions for stochastic local stability and stochastic evolutionary stability are established. Conditions for a fixation state to be stochastically unstable and almost everywhere stochastically unstable are distinguished in a multiphenotype setting according to the initial population state. Our results provide some alternative perspective and a more general theoretical framework for a better understanding of the evolution of animal behavior in a stochastic environment.

Evolutionary game dynamics with non-uniform interaction rates in finite population

In this study, we extend evolutionary game dynamics with non-uniform interaction rates to the situation with finite population. Our main goal is to show how the fixation probability is influenced by the non-uniform interaction rates under weak selection. Based on the diffusion approximation of the Moran process and assumption of weak selection, the stochastic dynamic properties of a two-phenotype game with non-uniform interaction rates in a finite population are investigated. By the analysis of some cases, we show that the non-uniform interaction rates may result in the potential evolutionary complexity of game dynamics in finite population.

A new approach considering temporal correlations for GPS campaign time series

GPS campaign-mode surveys are periodically collected measurements and their time series has a considerable percentage of data gaps unlike continuous time series. Studying error characteristics of a time series is imperative to compute reliable parameter uncertainties. The power-law process can best describe the background noise for a GPS continuous time series and may be introduced into the analysis through well-known methods. However, the power-law process cannot be applied successfully over GPS campaign time series due to the constraints mentioned above. Here we demonstrate a new approach enabling one to project the stochastic properties of campaign time series into the stochastic domain of the permanent stations of International GNSS Service (IGS) network. The stochastic domain, the combination of white noise (WN) and flicker noise (FN), was obtained from the power spectrum of a continuous time series consisting of truncated daily RINEX observations. We implemented it in the Python3 environment as an open-source package called GPS/GNSS campaign time series analysis (GCTS v1.0). The analysis showed that the velocity uncertainties may be, on average, underestimated by a factor of 2 when assuming the WN-only noise model using campaign data from the UNAVCO data archive collected in San Bernardino and its vicinity. Moreover, to reveal the progress of the new approach, we modelled buried screw dislocations of the San Jacinto, the San Andreas, and parallel faults in their vicinity in elastic half-space. When using the new approach with the combination of WN and FN instead of the WN-only model, we achieved a significant improvement of 15% on average in the chi-square value. Our outcomes showed that the noise process should be considered even for campaign time series. The proposed approach facilitates the analysis of GPS campaign time series even if they include considerable data gaps.

A modified Lattice Boltzmann method for predicting the effective thermal conductivity of open-cell foam materials

The heat transfer in porous media have attracted wide attention in various scientific studies. The microstructure model of open-cell foam is reconstructed using the random generation method satisfying the microstructure stochastic properties. A modified Lattice Boltzmann method (LBM) is proposed to resolve the heat transport equations for predicting effective thermal conductivity (ETC). The proposed LBM simulation introduces the additional coefficient to moderate the difference in dimensionless relaxation time between solid and gas phase. The modified LBM simulation reliability is validated by comparing with numerical models and available experimental results. Simulations are conducted to evaluate the effects of a larger range of porosity, ambient pressure, temperature and intrusion mediums on heat transfer. The results indicate that the 400 K is considered as a turning point in the ETC dependence on temperature. At low porosity, the ETC fluctuates more sharply compared to high porosity. The impact of ambient pressure on the ETC is divided into three levels: P < 10 kPa, the ETC is almost insensitive to pressure fluctuation; 10 kPa < P < 100 kPa, the ETC slightly increases with the pressure increase; P > 100 kPa, the ETC significantly increases. The proposed LBM simulation combined with the random generation method is an efficient tool to predict the heat transfer for open-cell foam.

Representation of 3-h Offshore Short-Crested Wave Field in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

Abstract Stochastic wave properties are crucial for the design of offshore structures. Short-crested seas are commonly seen at the sites of offshore structures, especially during storm events. A long time duration is required in order to obtain the statistical properties, which is challenging for numerical simulations. In this scenario, a potential flow solver is ideal due to its computational efficiency. A procedure of reproducing accurate short-crested sea states using the open-source fully nonlinear potential flow model REEF3D::FNPF is presented in the paper. The procedure examines the sensitivity of the resolutions in space and time as well as the arrangements of wave gauge arrays. A narrow band power spectrum and a mildly spreading directional spreading function are simulated, and an equal energy method is used to generate input waves and avoid phase-locking. REEF3D::FNPF solves the Laplace equation together with the boundary conditions using a finite difference method. A sigma grid is used in the vertical direction and the vertical grid clustering follows the principle of constant truncation error. High-order discretization methods are implemented in space and time. Message passing interface is used for high performance computation using multiple processors. Three-hour simulations are performed in full-scale at a hypothetic offshore site with constant water depth. The significant wave height, peak period, kurtosis, skewness and ergodicity are examined in the numerically generated wave field. The stochastic wave properties in the numerical wave tank (NWT) using REEF3D::FNPF match the input wave conditions with high fidelity.

A direct method to detect deterministic and stochastic properties of data

A fundamental question of data analysis is how to distinguish noise corrupted deterministic chaotic dynamics from time-(un)correlated stochastic fluctuations when just short length data is available. Despite its importance, direct tests of chaos vs stochasticity in finite time series still lack of a definitive quantification. Here we present a novel approach based on recurrence analysis, a nonlinear approach to deal with data. The main idea is the identification of how recurrence microstates and permutation patterns are affected by time reversibility of data, and how its behavior can be used to distinguish stochastic and deterministic data. We demonstrate the efficiency of the method for a bunch of paradigmatic systems under strong noise influence, as well as for real-world data, covering electronic circuit, sound vocalization and human speeches, neuronal activity, heart beat data, and geomagnetic indexes. Our results support the conclusion that the method distinguishes well deterministic from stochastic fluctuations in simulated and empirical data even under strong noise corruption, finding applications involving various areas of science and technology. In particular, for deterministic signals, the quantification of chaotic behavior may be of fundamental importance because it is believed that chaotic properties of some systems play important functional roles, opening doors to a better understanding and/or control of the physical mechanisms behind the generation of the signals.

Water surge impingement onto a vertical wall: Laboratory experiments and stochastic analysis on impact pressure

This study aimed to propose a stochastic model for the impact pressure generated by water surge impingement onto a vertical wall. Carefully controlled laboratory experiments were conducted in a small-scale flume under four different surge conditions. Using pressure sensors and a high-speed video camera, we repeatedly measured the surge-induced pressures on the wall together with the surge parameters right before impingement, e.g. the surge front velocity and slope, under each condition. The impact pressure tended to increase linearly with the squared surge front velocity but with high data scattering, reflecting its stochastic nature. Meanwhile, it exhibited limited dependency on the surge front slope, especially at the bottom of the wall, contrary to Cumberbatch's theory of surge impact pressure. We investigated the stochastic properties of the impingement process from the experimental data and proposed a stochastic model of the impact pressure based on an extreme value probability distribution (the Fréchet distribution). The proposed model, which involved only the surge front velocity, fit well with the present dataset and experimental data randomly collected from various literature works. We confirmed that the predictive model is potentially applicable to a wide range of surge impingement problems.

Topological homogenization of metamaterial variability

With the proliferation of additive manufacturing and 3D printing technologies, a broader palette of material properties can be elicited from cellular solids, also known as metamaterials, architected foams, programmable materials, or lattice structures. Metamaterials are designed and optimized under the assumption of perfect geometry and a homogeneous underlying base material. Yet in practice real lattices contain thousands or even millions of complex features, each with imperfections in shape and material constituency. While the role of these defects on the mean properties of metamaterials has been well studied, little attention has been paid to the stochastic properties of metamaterials, a crucial next step for high reliability aerospace or biomedical applications. In this work we show that it is precisely the large quantity of features that serves to homogenize the heterogeneities of the individual features, thereby reducing the variability of the collective structure and achieving effective properties that can be even more consistent than the monolithic base material. In this first statistical study of additive lattice variability, a total of 239 strut-based lattices were mechanically tested for two pedagogical lattice topologies (body centered cubic and face centered cubic) at three different relative densities. The variability in yield strength and modulus was observed to exponentially decrease with feature count (to the power −0.5), a scaling trend that we show can be predicted using an analytic model or a finite element beam model. The latter provides an efficient pathway to extend the current concepts to arbitrary/complex geometries and loading scenarios. These results not only illustrate the homogenizing benefit of lattices, but also provide governing design principles that can be used to mitigate manufacturing inconsistencies via topological design.