Search Results (25)

Time series data are fundamental for analyzing temporal dynamics and patterns, enabling researchers and practitioners to model, forecast, and support decision-making across a wide range of domains, such as finance, climate science, environmental studies, and signal processing. In the context of high-dimensional time series, the Vector Autoregressive model (VAR) is widely used, wherein each variable is modeled as a linear combination of lagged values of all variables in the system. However, the traditional VAR framework relies on the assumption of stationarity, which states that the autoregressive coefficients remain constant over time. Unfortunately, this assumption often fails in practice, especially in systems subject to structural breaks or evolving temporal dynamics. The Time-Varying Vector Autoregressive (TV-VAR) model has been developed to address this limitation, allowing model parameters to vary over time and thereby offering greater flexibility in capturing non-stationary behavior. In this study, we propose an enhanced modeling approach for the TV-VAR framework by incorporating minimization solvers in generalized additive models and one-sided kernel smoothing techniques. The effectiveness of the proposed methodology is assessed using simulations based on non-homogeneous Markov chains, accompanied by a detailed discussion of its advantages and limitations. Finally, we illustrate the practical utility of our approach using an application to real-world financial data. Full article

Bitcoin’s role in global finance has rapidly expanded with increasing institutional participation, prompting new questions about its linkage to macroeconomic variables. This study thoughtfully integrates a Bayesian Markov Chain Monte Carlo (MCMC) covariate selection process within homogeneous and non-homogeneous Hidden Markov Models (HMMs) to analyze 16 macroeconomic and Bitcoin-specific factors from 2016 to 2024. The proposed method integrates likelihood penalties to refine variable selection and employs a rolling-window bootstrap procedure for 1-, 5-, and 30-step-ahead forecasting. Results indicate a fundamental shift: while early Bitcoin pricing was primarily driven by technical and supply-side factors (e.g., halving cycles, trading volume), later periods exhibit stronger ties to macroeconomic indicators such as exchange rates and major stock indices. Heightened volatility aligns with significant events—including regulatory changes and institutional announcements—underscoring Bitcoin’s evolving market structure. These findings demonstrate that integrating Bayesian MCMC within a regime-switching model provides robust insights into Bitcoin’s deepening connection with traditional financial forces. Full article

This review article is concerned to provide a global context to several works on the fitting of continuous time nonhomogeneous Markov chains with finite state space and also to point out some selected aspects of two techniques previously introduced—estimation and calibration—relevant for applications and used to fit a continuous time Markov chain model to data by the adequate selection of parameters. The denomination estimation suits the procedure better when statistical techniques—e.g., maximum likelihood estimators—are employed, while calibration covers the case where, for instance, some optimisation technique finds a best approximation parameter to ensure good model fitting. For completeness, we provide a short summary of well-known important notions and results formulated for nonhomogeneous Markov chains that, in general, can be transferred to the homogeneous case. Then, as an illustration for the homogeneous case, we present a selected Billingsley’s result on parameter estimation for irreducible chains with finite state space. In the nonhomogeneous case, we quote two recent results, one of the calibration type and the other with more of a statistical flavour. We provide an ample set of bibliographic references so that the reader wanting to pursue her/his studies will be able to do so more easily and productively. Full article

Modelling and predicting dairy cow diseases empowers farmers with valuable information for herd health management, thereby decreasing costs and increasing profits. For this purpose, predictive models were developed based on machine learning algorithms. However, machine-learning based approaches require the development of a specific model for each disease, and their consistency is limited by low farm data availability. To overcome this lack of complete and accurate data, we developed a predictive model based on discrete Homogeneous and Non-homogeneous Markov chains. After aggregating data into categories, we developed a method for defining the adequate number of Markov chain states. Subsequently, we selected the best prediction model through Chebyshev distance minimization. For 14 of 19 diseases, less than 15% maximum differences were measured between the last month of actual and predicted disease data. This model can be easily implemented in low-tech dairy farms to project costs with antibiotics and other treatments. Furthermore, the model’s adaptability allows it to be extended to other disease types or conditions with minimal adjustments. Therefore, including this predictive model for dairy cow diseases in decision support systems may enhance herd health management and streamline the design of evidence-based farming strategies. Full article

We propose a method for fitting transition intensities to a sufficiently large set of trajectories of a continuous-time non-homogeneous Markov chain with a finite state space. Starting with simulated data computed with Gompertz–Makeham transition intensities, we apply the proposed method to fit piecewise linear intensities and then compare the transition probabilities corresponding to both the Gompertz–Makeham transition intensities and the fitted piecewise linear intensities; the main comparison result is that the order of magnitude of the average fitting error per unit time—chosen as a year—is always less than 1%, thus validating the methodology proposed. Full article

In the present, we study the problem of strong ergodicity in nonhomogeneous Markov systems. In the first basic theorem, we relax the fundamental assumption present in all studies of asymptotic behavior. That is, the assumption that the inherent inhomogeneous Markov chain converges to a homogeneous Markov chain with a regular transition probability matrix. In addition, we study the practically important problem of the rate of convergence to strong ergodicity for a nonhomogeneous Markov system (NHMS). In a second basic theorem, we provide conditions under which the rate of convergence to strong ergodicity is geometric. With these conditions, we in fact relax the basic assumption present in all previous studies, that is, that the inherent inhomogeneous Markov chain converges to a homogeneous Markov chain with a regular transition probability matrix geometrically fast. Finally, we provide an illustrative application from the area of manpower planning. Full article

Entropy measures the randomness or uncertainty of a stochastic process, and the entropy rate refers to the limit of the time average of entropy. The generalized entropy rate in the form of delayed averages can overcome the redundancy of initial information while ensuring stationarity. Therefore, it has better practical value. A Hidden Markov Model (HMM) contains two stochastic processes, a stochastic process in which all states can be observed and a Markov chain in which all states cannot be observed. The entropy rate is an important characteristic of HMMs. The transition matrix of a homogeneous HMM is unique, while a Nonhomogeneous Hidden Markov Model (NHMM) requires the transition matrices to be dependent on time variables. From the perspective of model structure, NHMMs are novel extensions of homogeneous HMMs. In this paper, the concepts of the generalized entropy rate and NHMMs are defined and fully explained, a strong limit theorem and limit properties of a norm are presented, and then generalized entropy ergodic theorems with an almost surely convergence for NHMMs are obtained. These results provide concise formulas for the computation and estimation of the generalized entropy rate for NHMMs. Full article

In a networked control system scenario, the packet dropout is usually modeled by a time-invariant (homogeneous) Markov chain (MC) process. However, from a practical point of view, the probabilities of packet loss can vary in time and/or probability parameter dependency. Therefore, to design a fault detection filter (FDF) implemented in a semi-reliable communication network, it is important to consider the variation in time of the network parameters, by assuming the more accurate scenario provided by a nonhomogeneous jump system. Such a premise can be properly taken into account within the linear parameter varying (LPV) framework. In this sense, this paper proposes a new design method of ${\mathcal{H}}_{\infty }$ gain-scheduled FDF for Markov jump linear systems under the assumption of a nonhomogeneous MC. To illustrate the applicability of the theoretical solution, a numerical simulation is presented. Full article

The resource network is a non-linear threshold model where vertices exchange resource in infinite discrete time. The model is represented by a directed weighted graph. At each time step, all vertices send their resources along all output edges following one of two rules. For each vertex, the threshold value for changing the operation rule is equal to the total weight of its outgoing edges. If all vertices have resources less than their thresholds, the network is completely described by a homogeneous Markov chain. If at least one of the vertices has a resource above the threshold, the network is described by a non-homogeneous Markov chain. The purpose of this article is to describe and investigate non-homogeneous Markov chains generated by the resource network model. It is proven that they are strongly ergodic. In addition, stochastic matrices of a special form were studied. A number of new properties were revealed for them. The results obtained were generalized to arbitrary stochastic matrices. Full article

The sustainable management of the water supply system requires methodologies to monitor, repair, or replace the aging infrastructure, but more importantly, it must be able to assess the condition of the networks and predict their behavior over time. Among other infrastructure systems, the water distribution network is one of the essential civil infrastructure systems; therefore, the effective maintenance and renewal of the infrastructure’s physical assets are essential. This article aims to determine pipe failure prediction to optimize pipe renewal time. This research methodology investigates the most appropriate parameters for predicting pipe failure in the optimization. In particular, the non-homogeneous Poisson process (NHPP) with the Markov chain Monte Carlo (MCMC) approach is presented for Bayesian inference, while maximum likelihood (ML) is applied for frequentist inference as a comparison method. It is concluded that the two estimations are relatively appropriate for predicting failures, but MCMC estimation is closer to the total observed data. Based on life-cycle cost (LCC) analysis, the MCMC estimation generates flatter LCC curves and lower LCC values than the ML estimation, which affects the decision making of optimum pipe renewal in water distribution networks. Full article

Since the regulatory relationship between genes is usually non-stationary, the homogeneity assumption cannot be satisfied when modeling with dynamic Bayesian networks (DBNs). For this reason, the homogeneity assumption in dynamic Bayesian networks should be relaxed. Various methods of combining multiple changepoint processes and DBNs have been proposed to relax the homogeneity assumption. When using a non-homogeneous dynamic Bayesian network to model a gene regulatory network, it is inevitable to infer the changepoints of the gene data. Based on this analysis, this paper first proposes a data-based birth move (ED-birth move). The ED-birth move makes full use of the potential information of data to infer the changepoints. The greater the Euclidean distance of the mean of the data in the two components, the more likely this data point will be selected as a new changepoint by the ED-birth move. In brief, the selection of the changepoint is proportional to the Euclidean distance of the mean on both sides of the data. Furthermore, an improved Markov chain Monte Carlo (MCMC) method is proposed, and the improved MCMC introduces the Pearson correlation coefficient (PCCs) to sample the parent node-set. The larger the absolute value of the Pearson correlation coefficient between two data points, the easier it is to be sampled. Compared with other classical models on Saccharomyces cerevisiae data, synthetic data, RAF pathway data, and Arabidopsis data, the PCCs-ED-DBN proposed in this paper improves the accuracy of gene network reconstruction and further improves the convergence and stability of the modeling process. Full article

This paper examines the fault-tolerant control problem for discrete-time descriptor systems that are susceptible to intermittent actuator failures, nonlinear sensor data, and probability-based missing data. The discrete-time non-homogeneous Markov chain was adopted to describe the stochastic behavior of actuator faults. Moreover, Bernoulli-distributed stochastic variables with known conditional probabilities were employed to describe the practical features of random sensor non-linearity and missing data. In this study, the output signals were quantized and a dynamic output feedback controller was synthesized such that the closed-loop system was stochastically admissible and satisfied the strictly $(\mathbf{Q},\mathbf{S},\mathbf{R})$-$\gamma$-dissipative performance index. The theoretical developments are illustrated through numerical simulations of an infinite machine bus. Full article

An effective integrated design optimization method is developed to reduce the maximum von Mises stress around vent holes of a high-pressure turbine sealing disk. It mainly includes four different shape designs (circular, elliptical, race-track, and four-arc) for holes, an updated self-developed modelling and meshing tool, an APDL-based strength analysis, and a self-proposed efficient switching delayed particle swarm optimization (SDPSO) algorithm. The main idea of SDPSO is: (1) by evaluating an evolutionary factor and utilizing a probability transition matrix, a non-homogeneous Markov chain is determined and auto-updated in each generation; (2) the evolutionary factor and the Markov chain are used to adaptively select the inertia weight, acceleration coefficients, and delayed information to adjust the particle’s velocity. The performance of SDPSO is evaluated through two benchmark optimization problems with constraints. The results show that SDPSO is superior to two well-known PSO algorithms in optimization capability, numerical robustness, and convergence speed. Furthermore, SDPSO is used for the stress optimization of vent holes with four different shapes. The results show that: (1) SDPSO is suitable and valuable for practical engineering optimization problems with constraints; (2) the developed integrated design optimization method is effective and advanced for reducing the maximum von Mises stress around the vent holes; and (3) the four-arc hole has more tremendous advantages in reducing the maximum von Mises stress, followed by the elliptical hole, the race-track hole, and the circular hole. Full article

Information diffusion, information spread, and influencers are important concepts in many studies on social media, especially Twitter analytics. However, literature overviews on the information diffusion of Twitter analytics are sparse, especially on the use of continuous time Markov chain (CTMC). This paper examines the following topics: (1) the purposes of studies about information diffusion on Twitter, (2) the methods adopted to model information diffusion on Twitter, (3) the metrics applied, and (4) measures used to determine influencer rankings. We employed a systematic literature review (SLR) to explore the studies related to information diffusion on Twitter extracted from four digital libraries. In this paper, a two-stage analysis was conducted. First, we implemented a bibliometric analysis using VOSviewer and R-bibliometrix software. This approach was applied to select 204 papers after conducting a duplication check and assessing the inclusion–exclusion criteria. At this stage, we mapped the authors’ collaborative networks/collaborators and the evolution of research themes. Second, we analyzed the gap in research themes on the application of CTMC information diffusion on Twitter. Further filtering criteria were applied, and 34 papers were analyzed to identify the research objectives, methods, metrics, and measures used by each researcher. Nonhomogeneous CTMC has never been used in Twitter information diffusion modeling. This finding motivates us to further study nonhomogeneous CTMC as a modeling approach for Twitter information diffusion. Full article

In the design stage of energy systems in buildings, accurate load boundary conditions are the key to achieving energy supply and demand balance. Compared with the building cold and heat load, the generation of building electrical load has stronger randomness, and the current standard electrical load calculation method cannot reflect this feature. Therefore, this paper proposes a bottom-up high time resolution power load generation method for office buildings. Firstly, the non-homogeneous Markov chain is used to establish the random mobility model of personnel in office buildings, and the building electrical appliances are divided into four categories according to the different driving modes of personnel to electrical appliances in office buildings. Then, based on the personnel mobility model, the correlation between the use of electrical appliances in office buildings and the personnel in the room is established to construct the random power simulation model of different types of electrical appliances. Finally, the electric load of different types of electrical appliances is superimposed hourly to generate a random daily load curve. In order to verify the validity of the model, an office building is simulated and compared with the measured electrical load value. The verification results show that the model well reflects the daily distribution characteristics of electric load. The simulation value and the measured value are used for statistical analysis. The evaluation results show that the correlation between the simulation value and the measured value is high, which further illustrates the validity and accuracy of the model. Full article