Non-stationary Research Articles

К МЕТОДИКЕ ФОРМИРОВАНИЯ ЦИФРОВОГО ДВОЙНИКА ТЕХНОЛОГИЧЕСКОГО ПРОЦЕССА СУШКИ ОРГАНИЧЕСКИХ СЕМЯН ТИМОФЕЕВКИ

An important specific feature of the functioning of machines and equipment in the technologies of post-harvest processing of grain and seeds is the probabilistic variability of external conditions that negatively affect the efficiency of their work. The drying process is also characterized by non-stationarity in its probabilistic and statistical characteristics. The methods of forming digital twins of stationary processes are quite well mastered, but the construction of digital twins of non-stationary processes is a much more complex task, the solution of which requires taking into account the nature of non-stationarity, as well as the features and internal structure of the processes being modeled. The purpose of the research is to build a digital twin of the non-stationary process of drying timothy seeds and assess the reliability of the resulting model. The experimental data were obtained by drying Leningradskaya 204 timothy grass seeds from the field organic crop rotation using a universal drying unit with a Fauna PMDR4 digital seed moisture meter equipped with submersible flow sensors. As a result of the experimental studies, realizations of random processes of change in seed moisture content at the final stage of drying were obtained for constructing mathematical models using statistical identification methods. Discrete analogs of the processes under study were constructed using experimental correlation functions approximated by the corresponding functions to obtain the parameters of the modeling recurrent equations. The considered algorithm for modeling the dryer operation allows reproducing processes of unlimited length and modeling various conditions and operating modes to find the specified optima for quality, energy consumption and environmental friendliness. The accuracy of the simulation results was determined based on the convergence of the moment functions of the experimental and modeled technological processes. Estimates of statistical characteristics of the simulated process of drying timothy grass seeds with 95% probability correspond to statistical estimates of the drying process obtained in the course of experimental studies, and the graphs of their normalized correlation functions clearly confirm the identity of the processes. The obtained mathematical dependencies of the technological process of drying organic timothy grass seeds are its digital twin, allowing the methods of simulation modeling to solve optimization problems.

Jensen-autocorrelation function for weakly stationary processes and applications

The Jensen-variance (JV) information based on Jensen’s inequality and variance has been previously proposed to measure the distance between two random variables. Based on the relationship between JV distance and autocorrelation function of two weakly stationary process, the Jensen-autocovariance and Jensen-autocorrelation functions are proposed in this paper. Furthermore, the distance between two different weakly stationary processes is measured by the Jensen-cross-correlation function. Moreover, autocorrelation function is also considered for ARMA and ARFIMA processes, deriving explicit formulas for Jensen-autocorrelation function that only depends on model parametric space and lag, whose were also illustrated by numeric results. In order to study the usefulness of proposed functions, two real-life applications were considered: the Tree Ring and Southern Humboldt current ecosystem time series.

On Lamperti transformation and AR(1) type characterisations of discrete random fields

In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and, through Lamperti transformation, self-similar fields. Our contribution is a natural generalisation of recently proved results covering the case of stationary processes.

A non-linear integer-valued autoregressive model with zero-inflated data series

A new non-linear stationary process for time series of counts is introduced. The process is composed of the survival and innovation component. The survival component is based on the generalized zero-modified geometric thinning operator, where the innovation process figures in the survival component as well. A few probability distributions for the innovation process have been discussed, in order to adjust the model for observed series with the excess number of zeros. The conditional maximum likelihood and the conditional least squares methods are investigated for the estimation of the model parameters. The practical aspect of the model is presented on some real-life data sets, where we observe data with inflation as well as deflation of zeroes so we can notice how the model can be adjusted with the proper parameter selection.

Modelling ℤ-valued time series with Skellam thinning-based INAR(1) process

ABSTRACT Non-stationary count time series, which are small in value and show a trend having relatively large fluctuation, are commonly encountered in real-world applications. Differencing is a commonly employed method to transform a non-stationary time series into a stationary one. However, the differenced count time series is defined on Z and cannot be fitted by the mainstream count time series models, which are defined on N 0 . Although some integer-valued autoregressive (INAR) models based on the signed thinning operator have been proposed for fitting Z -valued time series, these models still encounter difficulties in terms of data generation mechanism, model selection, and parameter estimation. These difficulties may pose challenges for practitioners in practical applications. Therefore, this article utilizes the reparameterized version of the Skellam (Poisson difference) distribution to construct a new thinning operator, thereby introducing a class of Z -valued time series models. Strict stationarity, ergodicity, statistical properties, and parameter estimation methods of the processes are detailedly discussed. An application to the monthly counts of newly listed companies illustrates that the new model is superior in data analysis of finance and economics.

On the evaluation of accretion process near a quantum-improved charged black hole

This paper deals with astrophysical accretion onto the quantum-improved charged black hole. An accretion process does not depend on time; it is a stationary process. In this analysis, we explore the physical quantities like energy density, radial velocity, sonic speed, and accretion mass rate for quantum-improved charged black holes and compare them with the existing outcomes corresponding to the Schwarzschild black hole. Following the Michel and Babichev approaches, we investigate the quantities mentioned above by taking into account different equations of state. These fundamental approaches and black hole parameters are responsible for decreasing the fluid's radial infalling velocity during the accretion process and, for others, as a gravitational enhancer, increasing the fluid flow into the black hole horizon. The polytropic fluid's accretion process is also discussed. All the quantities are analyzed graphically with a contour structure. It is observed that the maximum accretion rate is achieved for different values of the considered black hole parameters. From this analysis, we may be able to understand the physical mechanism of accretion onto a quantum-improved charged black hole.

Frequency domain local bootstrap in short and long memory time series

Bootstrap methods in the frequency domain are effective instruments to approximate the distribution of many statistics of weakly dependent (short memory) series but their validity with long memory remains mostly unsolved. This article proposes a frequency domain local bootstrap (FDLB) based on resampling a locally studentized version of the periodogram in a neighborhood of the frequency of interest. A bound of the Mallows distance between the distributions of the periodogram and its FDLB bootstrap counterpart is offered for anti-persistent, weakly dependent, stationary, and non stationary long memory series. This result is in turn used to justify the use of the FDLB for some statistics that are weighted averages of periodogram ordinates. Finally, the validity of the FDLB to estimate the distribution of the local Whittle estimator is proved and its finite sample behavior analyzed in a Monte Carlo and in an empirical application, comparing its performance with rival alternatives.

A Stationary Proportional Hazard Class Process and its Applications

A Stationary Proportional Hazard Class Process and its Applications

Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains

This article investigates the expectation and autocorrelation functions of random processes in the discrete-Fresnel and the discrete-frequency domains, originating from wide-sense stationary (WSS) random processes in the discrete-time domain. Through mathematical deduction, it is demonstrated that WSS random processes in the discrete-time domain exhibit the same expectation and autocorrelation functions as transformed to the discrete-Fresnel domain. In contrast, this property is not observed in the discrete-frequency domain. White, pink, and brown random processes are considered to illustrate these behaviors in the discrete-Fresnel and discrete-frequency domains. Furthermore, this study numerically compares data communication systems based on single-carrier with cyclic prefix, orthogonal chirp-division multiplexing, and orthogonal frequency-division multiplexing schemes, which are respectively designed in the discrete-time, discrete-Fresnel, and discrete-frequency domains. The numerical results show that orthogonal chirp-division multiplexing and single-carrier with cyclic prefix schemes achieve comparable communication performance under any additive noise modeled by a wide-sense stationary random process, regardless of the chosen linear equalization or the absence of it.

Discrete Analysis of Electrical Circuit with Sources of Rectangular Pulses

Abstract Discrete transients and stationary process are described in series RC-circuits when the supplied voltage contains periodic rectangular pulses. The analysis is performed using z - transformation to obtain analytical dependencies for the capacitive voltage in any time of the rectangular pulses. The approach is used for discrete analysis of various circuits in which rectangular pulses have different characteristics. The calculated capacitive voltages by the obtained discrete dependencies are identical, compared to the results obtained by SPICE simulation. The method proposed in the present work allows, together with the transient process, to investigate the corresponding stationary process. Cases of stable and unstable transients are shown.

Deconvolution of ℙ(Xt < Yt ) for stationary processes with supersmooth error distributions

This paper focuses on nonparametrically estimating the probability P ( X t < Y t ) when two strongly mixing stationary processes, X t and Y t , are observed with additional errors at discrete time points t j = j Δ (where Δ is a positive constant). This problem has practical significance in some applications where data is time-dependent random variable sequences (generated from stochastic processes) like time-dependent stress–strength reliability modelling and receiver operating characteristic (ROC) curve analysis. We extend our analysis to account for errors generated from another strongly mixing stationary processes and derive convergence rate and asymptotic normality results for the estimator under supersmooth error distributions. Through applications and simulations, we illustrate the properties of our estimator.

Mixed orthogonality graphs for continuous-time stationary processes

In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent characterisations are given for the different definitions, in particular by orthogonal projections. We then define two mixed graphs based on different definitions of Granger causality and contemporaneous correlation, the (mixed) orthogonality graph and the local (mixed) orthogonality graph. In these graphs, the components of the process are represented by vertices, directed edges between the vertices visualise Granger causal influences and undirected edges visualise contemporaneous correlation between the component processes. Further, we introduce various notions of Markov properties in analogy to Eichler (2012), which relate paths in the graphs to different dependence structures of subprocesses, and we derive sufficient criteria for the (local) orthogonality graph to satisfy them. Finally, as an example, for the popular multivariate continuous-time AR (MCAR) processes, we explicitly characterise the edges in the (local) orthogonality graph by the model parameters.

Spatial queues with nearest neighbour shifts

This work studies queues in a Euclidean space. Consider N servers that are distributed uniformly in [0,1]d. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide whether to join the queue they arrived at, or shift to one of the nearest neighbours. Such shifting strategies affect the load on the servers, and may cause some of the servers to become overloaded. We derive a law of large numbers and a central limit theorem for the fraction of overloaded servers in the system as the total number of servers N→∞. Additionally, in the one-dimensional case (d=1), we evaluate the expected fraction of overloaded servers for any finite N. Numerical experiments are provided to support our theoretical results. Typical applications of the results include electric vehicles queueing at charging stations, and queues in airports or supermarkets.

Stochastic analysis of combined primary-secondary structures subjected to imprecise seismic excitation

The imprecise stochastic process model is able to incorporate both random and epistemic uncertainties, leading to a more accurate description of environmental excitations, such as earthquakes or wind loads, when limited data are available. Epistemic uncertainties in the loading model may significantly affect the performance of structural systems.The present paper addresses the stochastic analysis of combined primary-secondary structures subjected to imprecise seismic excitation modeled as a zero-mean stationary Gaussian random process, characterized by an interval-valued Power Spectral Density (PSD) function. The power and energy content of the imprecise ground motion acceleration may vary, even for the same soil category, affecting the complex dynamic behavior of combined structures and the vibration control capacity of secondary substructures under different frequency tuning conditions. The main purpose of this study is to develop a framework for investigating both the influence of epistemic uncertainties in the loading model and the interaction effects between the subsystems on the seismic performance of combined primary-secondary structures. To this aim, the stochastic analysis of combined structures under imprecise ground motion acceleration is addressed in both the frequency and time domains by an efficient approach capable of decoupling the propagation of interval and random uncertainties. Seismic safety assessment is performed in the framework of the first-passage theory by interval extension.

Trends in temperature data: Micro-foundations of their nature

Determining whether Global Average Temperature (GAT) is an integrated process of order 1, I(1), or a stationary process around a trend function is crucial for detection, attribution, impact, and forecasting studies of climate change. In this paper, we investigate the nature of trends in GAT building on the analysis of individual temperature grids. Our micro-founded evidence suggests that GAT is stationary around a non-linear deterministic trend in the form of a linear function with one structural break. This break can be attributed to a combination of breaks on individual grids and the standard aggregation method under acceleration in global warming.

Transitions between equilibrium and nonequilibrium phenomena in the description of crystal growth

The close intertwining of equilibrium and nonequilibrium thermodynamic representations and transitions between the two limiting principles of thermodynamics: the second beginning and the principle of least coercion (minimum entropy production in the stationary regime) constitute the main content of phenomenological theories of crystal growth. The difference of basic postulates of two sections of thermodynamics forces to discuss problems of reversibility and irreversibility of time, scales of observed phenomena and rules of conjugation of thermodynamic forces and flows in theories of crystal growth. A variant of the solution of some conjugation problems is shown on the example of the fluctuation model of dislocation crystal growth, which is based on the stationary isothermal process of thermodynamic free energy fluctuations. In the case of the limiting mode of adsorption of impurities on the crystal face according to the Langmuir model, the free energy fluctuations possessing the absence of the memory effect allow us to identify three chemical potentials of building particles that determine the corresponding values of solution supersaturations realized at different scale levels at the growing crystal face containing a helical dislocation. The supersaturations control quasi-equilibrium and nonequilibrium thermodynamic processes that constitute a single dislocation mechanism of crystal growth.

Theoretical study of the working process of a multivariate cabbage harvester

BACKGROUND. A multi-variant cabbage harvester of a block-modular design is proposed for small-scale farming in vegetable growing. At the same time, it is planned to complete the cabbage harvester in three versions: with an elevator, with a lower longitudinal conveyor, with an elevator and an upper longitudinal conveyor. AIMS – modeling the working process of a multivariate cabbage harvester to identify its main technological parameters that ensure the efficiency of its operation. MATERIALS AND METHODS. The working process of a multivariate cabbage harvester is presented as the functioning of a certain physical system, the state of which changes during the technological process over time depending on stochastic factors. The process of sequential transition of a system from one state to another is considered on the basis of queuing theory depending on the intensity of movement of the flow of heads of cabbage λ in the technological line of the machine and the intensity of service μ of this flow. In this work, the limiting probabilities of the model states are determined and the stochastic indicators of its functioning are calculated. RESULTS AND DISCUSSION. Based on the results of calculations of stochastic indicators of the functioning of the model, the optimal number of service personnel people was established, when the maximum probability of servicing cabbage heads can be up to 0.934. CONCLUSIONS. The workflow of a multivariate cabbage harvester is modeled as a stationary stochastic queuing process. Based on the research results, it is recommended to take the number of service personnel at the combine refining table as .

Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations

AbstractIn this paper we study the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of $$\mathbb {R}^n$$ R n . Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat (Res Notes Math III, 1982). In analogy to the random setting recently introduced by Giunti, Höfer and Velázquez (Commun Part Differ Equ 43(9):1377–1412, 2018) to study the Poisson equation, we only require that the random radii have finite $$(n-q)$$ ( n - q ) -moment, where $$1&lt;q&lt;n$$ 1 &lt; q &lt; n is the growth-exponent of the associated energy functionals. This assumption on the one hand ensures that the expectation of the nonlinear q-capacity of the spherical holes is finite, and hence that the limit problem is well defined. On the other hand, it does not exclude the presence of balls with large radii, that can cluster up. We show however that the critical rescaling of the perforations is sufficient to ensure that no percolating-like structures appear in the limit.

Bootstrap inference for linear time-varying coefficient models in locally stationary time series

Time-varying coefficient models can capture evolving relationships. However, constructing asymptotic confidence bands for coefficient curves in these models is challenging due to slow convergence rates and the presence of various nuisance parameters. A residual-based sieve bootstrap method has recently been proposed to address these issues. While it successfully produces confidence bands with accurate empirical coverage, its applicability is restricted to strictly stationary processes. We introduce a new bootstrap scheme, the local blockwise wild bootstrap (LBWB), that allows for locally stationary processes. The LBWB can replicate the distribution of the parameter estimates while automatically accounting for nuisance parameters. An extensive simulation study reveals the superior performance of the LBWB compared to various benchmark approaches. It also shows the potential applicability of the LBWB in broader scenarios, including time-varying cointegrating models. We then examine herding effects in the Chinese renewable energy market using the proposed methods. Our findings strongly support the presence of herding behaviors before 2016, aligning with earlier studies. However, contrary to previous research, we find no significant evidence of herding between around 2018 and 2021. Online supplementary materials are available for this article.

Stationary covariance regime for affine stochastic covariance models in Hilbert spaces

This paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order p∈[1,2]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p \\in [1,2]$\\end{document}, and give explicit formulas for the first two moments of the limit distribution. Our results allow us to introduce affine stochastic covariance models in the stationary covariance regime and to investigate the behaviour of the implied forward volatility for large forward dates in commodity forward markets.