Search Results (8)

The increasing complexity and uncertainty associated with high renewable energy penetration require forecasting methods that provide more comprehensive information for risk analysis and energy management. This paper proposes a novel probabilistic forecasting model for solar power generation based on a non-homogeneous multi-observation Hidden Markov Model (HMM). The model is purely data-driven, free from restrictive assumptions, and features a lightweight structure that enables fast updates and transparent reasoning—offering a practical alternative to computationally intensive neural network approaches. The proposed framework is first formalized through an extension of the classical HMM and the derivation of its core inference procedures. A method for estimating the probability density distribution of solar power output is introduced, from which point forecasts are extracted. Thirteen model variants with different observation-dependency structures are constructed and evaluated using real PV operational data. Experimental results validate the model’s effectiveness in generating both prediction intervals and point forecasts, while also highlighting the influence of observation correlation on forecasting performance. The proposed approach demonstrates strong potential for real-time solar power forecasting in modern power systems, particularly where speed, adaptability, and interpretability are critical. 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

The COVID-19 pandemic led to a surge in interest among scholars and public health professionals in identifying the predictors of health shocks and their transmission in the population. With temperature increases becoming a persistent climate stress, our aim is to evaluate how temperature specifically impacts the incidences of contagious disease. Using annual data from 1 AD to 2021 AD on the incidence of contagious disease and temperature anomalies, we apply both parametric and nonparametric modelling techniques and provide estimates of the contemporaneous, as well as lagged, effects of temperature anomalies on the spread of contagious diseases. A nonhomogeneous hidden Markov model is then applied to estimate the time-varying transition probabilities between hidden states where the transition probabilities are governed by covariates. For all empirical specifications, we find consistent evidence that temperature anomalies have a statistically significant effect on the incidence of a contagious disease in any given year covered in the sample period. The best fit model further indicates that the contemporaneous effect of a temperature anomaly on the response variable is the strongest. As temperature predictions continue to become more accurate, our results indicate that such information can be used to implement effective public health responses to limit the spread of contagious diseases. These findings further have implications for designing cost effective infectious disease control policies for different regions of the world. Full article

This article explores the finite-time control problem associated with a specific category of non-homogeneous hidden semi-Markov jump systems. Firstly, a hidden semi-Markov model is designed to characterize the asynchronous interactions that occur between the true system mode and the controller mode, and emission probabilities are used to establish relationships between system models and controller modes. Secondly, a novel piecewise homogeneous method is introduced to tackle the non-homogeneous issue by taking into account the time-dependent transition rates for the jump rules between different modes of the system. Thirdly, an asynchronous controller is developed by applying Lyapunov theory along with criteria for stochastic finite-time boundedness, ensuring the specified $H_{\infty }$ performance level is maintained. Finally, the effectiveness of this method is verified through two simulation examples. 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

We study the Bitcoin and Ether price series under a financial perspective. Specifically, we use two econometric models to perform a two-layer analysis to study the correlation and prediction of Bitcoin and Ether price series with traditional assets. In the first part of this study, we model the probability of positive returns via a Bayesian logistic model. Even though the fitting performance of the logistic model is poor, we find that traditional assets can explain some of the variability of the price returns. Along with the fact that standard models fail to capture the statistic and econometric attributes—such as extreme variability and heteroskedasticity—of cryptocurrencies, this motivates us to apply a novel Non-Homogeneous Hidden Markov model to these series. In particular, we model Bitcoin and Ether prices via the non-homogeneous Pólya-Gamma Hidden Markov (NHPG) model, since it has been shown that it outperforms its counterparts in conventional financial data. The transition probabilities of the underlying hidden process are modeled via a logistic link whereas the observed series follow a mixture of normal regressions conditionally on the hidden process. Our results show that the NHPG algorithm has good in-sample performance and captures the heteroskedasticity of both series. It identifies frequent changes between the two states of the underlying Markov process. In what constitutes the most important implication of our study, we show that there exist linear correlations between the covariates and the ETH and BTC series. However, only the ETH series are affected non-linearly by a subset of the accounted covariates. Finally, we conclude that the large number of significant predictors along with the weak degree of predictability performance of the algorithm back up earlier findings that cryptocurrencies are unlike any other financial assets and predicting the cryptocurrency price series is still a challenging task. These findings can be useful to investors, policy makers, traders for portfolio allocation, risk management and trading strategies. Full article

With Bitcoin, Ether and more than 2000 cryptocurrencies already forming a multi-billion dollar market, a proper understanding of their statistical and financial properties still remains elusive. Traditional economic theories do not explain their characteristics and standard financial models fail to capture their statistic and econometric attributes such as their extreme variability and heteroskedasticity. Motivated by these findings, we study Bitcoin and Ether prices via a Non-Homogeneous Pólya Gamma Hidden Markov (NHPG) model that has been shown to outperform its counterparts in conventional financial data. The NHPG algorithm has good in-sample performance and identifies both linear and non-linear effects of the predictors. Our results indicate that all price series are heteroskedastic with frequent changes between the two states of the underlying Markov process. In a somewhat unexpected result, the Bitcoin and Ether prices, although correlated, are significantly affected by different variables. We compare long term to short term Bitcoin data and find that significant covariates may change over time. Limitations of the current approach—as expressed by the large number of significant predictors and the poor out-of-sample predictions—back earlier findings that cryptocurrencies are unlike any other financial asset and hence, that their understanding requires novel tools and ideas. Full article

In terms of climate change and precipitation, there is large interest in how large-scale climatic features affect regional rainfall amount and rainfall occurrence. Large-scale climate elements need to be downscaled to the regional level for hydrologic applications. Here, a new Nonhomogeneous Hidden Markov Model (NHMM) called the Bayesian-NHMM is presented for downscaling and predicting of multisite daily rainfall during rainy season over the Huaihe River Basin (HRB). The Bayesian-NHMM provides a Bayesian method for parameters estimation. The model avoids the risk to have no solutions for parameter estimation, which often occurs in the traditional NHMM that uses point estimates of parameters. The Bayesian-NHMM accurately captures seasonality and interannual variability of rainfall amount and wet days during the rainy season. The model establishes a link between large-scale meteorological characteristics and local precipitation patterns. It also provides a more stable and efficient method to estimate parameters in the model. These results suggest that prediction of daily precipitation could be improved by the suggested new Bayesian-NHMM method, which can be helpful for water resources management and research on climate change. Full article