ABSTRACT This paper introduces a threshold stochastic conditional duration (TSCD) model to capture regime‐switching behaviour in both the observed duration process and the latent process. Additionally, the model captures complex market dynamics using roller‐coaster‐shaped hazard functions derived from the extended generalised inverse Gaussian (EGIG) distribution. The model parameters are estimated using the simulation‐based maximum likelihood method implemented via the sampling importance resampling algorithm, and validated through a simulation study. The empirical analysis employs trade duration data from the Apple incorporated and Tesla incorporated stocks. The results demonstrate that the TSCD model incorporated with EGIG distribution effectively captures distinct regime‐switching behaviours in trade durations, characterised by different parameter sets across regimes in the in‐sample analysis, yielding the highest log‐likelihood value and the lowest Akaike information criterion and Bayesian information criterion scores amongst all benchmark models. For the out‐of‐sample forecasts, the TSCD EGIG model consistently achieved the strongest performance, ranking first in most of the evaluated loss functions (mean squared forecast error and quasi‐likelihood). The Diebold–Mariano test further provides robust evidence of significant differences in the relative predictive performance of the models. Time‐at‐risk forecasts across various risk levels are computed and evaluated using the Kupiec likelihood ratio test. Lastly, density forecasts are assessed through the probability integral transform technique.

ABSTRACT A novel methodology is proposed for jointly modeling the price dynamics of natural gas and electricity by integrating graph‐based Machine Learning and optimal transport theory. The framework combines visibility graph embeddings with the Wasserstein barycenter to uncover latent structures and asymmetric dependencies between the two interconnected energy markets. Log‐return time series are first transformed into visibility graphs and then embedded into high‐dimensional vector spaces, where complex temporal and structural patterns become more discernible. In the embedding space, an information‐driven Wasserstein barycenter is computed by optimizing the barycenter weights via Shannon entropy maximization. This procedure reveals an asymmetric balance between the two markets, with natural gas exerting a structurally dominant influence. To characterize the joint stochastic dynamics, a Gaussian Mixture Model is fitted to the thus determined unbalanced Wasserstein barycenter using maximum likelihood estimation via the Expectation–Maximization algorithm. An additional Gaussian component is introduced for each commodity to capture market‐specific behavior. The resulting model can be calibrated to match the first four moments of the empirical log‐return distributions and their observed correlation. Applied to Italian market data from 2019 to 2023, a period marked by extreme volatility and systemic shocks, the methodology accurately reproduces both common dynamics and idiosyncratic deviations. The analysis reveals that the entropy‐optimal barycentric weights are for natural gas and for electricity, highlighting a dominant role of the natural gas market in the joint representation. Compared with a comprehensive benchmark of GARCH‐type models, the proposed framework exhibits markedly superior empirical performance. The approach provides a robust, interpretable, and adaptable tool for risk analysis, derivative pricing, and the study of structural interactions across energy markets.

ABSTRACT In this paper, we focus on estimating some unknown parameters of a geometric bifractional Brownian motion. A geometric bifractional Brownian motion satisfies a stochastic differential equation driven by a bifractional Brownian motion. Firstly, using the method of quadratic variation for a Gaussian process and the maximum likelihood method, we give the estimators for the unknown parameters. Then, we prove the asymptotic properties of the estimators. Secondly, the Monte Carlo method is used for simulation. Compared with the single maximum likelihood estimation method, the results show that the method in this paper is effective, reliable, and superior. Finally, we conduct an empirical study of financial markets with real financial data from Danimer Scientific Inc‐A (DNMR.N). By using path simulation, Euclidean distance and out‐of‐sample forecasting compared to other classical models, we effectively validate the superiority of the model in this paper in describing financial time series.

ABSTRACT Technological learning and diffusion effects intrinsically drive the development of emerging technology capabilities. However, technological learning is fraught with significant uncertainty, and the spatiotemporal diffusion process across heterogeneous regions adds complexity to crafting effective adoption strategies. Existing research has seldom explored the multi‐regional diffusion modes of emerging technologies under such technological learning uncertainty. Accordingly, this study develops a multi‐regional system optimization model that endogenizes both uncertain technological learning and spatial diffusion effects. Through scenario simulations, the impacts of three distinct diffusion modes (one‐way, circular, and unintentional) on the adoption pathways of emerging technologies are analyzed and compared. The simulation results reveal that: (1) Reducing learning uncertainty, shortening inter‐regional distance, enhancing the technology diffusion effect, and policymakers adopting a more aggressive risk attitude can significantly promote the adoption of emerging technologies. (2) Following the technological spillover of an emerging technology, the diffusion of an existing technology can influence its diffusion path in all three modes. (3) The circular diffusion mode was the most economical strategy from a total system cost perspective and demonstrated the strongest resilience to the uncertainties associated with technological learning. These findings provide valuable theoretical insights for policymakers to design robust strategies for deploying emerging technologies across regions. This study contributes to a better understanding of the technology diffusion process under uncertainty and presents a framework for enhancing diffusion efficiency and mitigating systemic risks.

ABSTRACT Fatigue is the most common reliability failure mechanism and has been studied widely since the 19th century. Material specimens are used in laboratory experiments to obtain fatigue test data. An S‐N curve is used to depict the relationship between the stress (or strain) and the number of cycles to failure . Statistical methods are used to fit an S‐N relationship that can be used further to estimate properties of fatigue‐life and fatigue‐strength distributions. In particular, one can obtain estimates and confidence intervals for distribution quantiles and failure probabilities. Likelihood‐based and Bayesian inference methods are the foundational methods for statistical estimation and quantification of statistical uncertainty. Improvements in computing technology (hardware, software, and computational methods) have made it practicable to use these methods for important applications. This paper uses these foundational methods to model fatigue life and fatigue strength as a function of the experimental variables stress amplitude, mean stress, and stress ratio, extending and importantly improving methods currently used for such applications. We illustrate the methods with two different data sets. The first example is based on S‐N test data of a composite material widely used to manufacture wind turbine blades, where the fatigue‐life model is specified, and the fatigue‐strength is induced. The second example is based on S‐N test data of an aluminum alloy commonly used in aerospace applications. Because of the complicated features of the fatigue life data for this example, we use a specified fatigue‐strength model and show how it can be used to make inferences about the corresponding fatigue‐life model. Finally, we show how to use these multiple regression models to obtain constant‐life diagrams (CLDs), an engineering tool that provides a visual representation of the quantiles of a fatigue‐life distribution as a function of stress amplitude and mean stress. We compare CLDs based on multiple regression models with CLDs obtained by using separate simple regression models for each level of stress ratio.

ABSTRACT This article presents a novel extension of the GARCH model incorporating weighted liquidity, modeled by fractional Brownian motion. The existence of a stationary solution is proven, and the higher‐order moments are calculated to illustrate the statistical properties of the model. Analysis of the auto‐correlation function of the squared process confirms the long‐term memory characteristic of the model. Numerical simulations are employed to validate the theoretical findings, demonstrating the significance of the model in the financial market.

ABSTRACT Acceptance sampling plans (ASP) help practitioners economically and efficiently verify product quality, serving as a widely applied statistical quality control method. Among ASPs, the simplest form is the single sampling plan (SSP). Recently, acceptance sampling systems incorporating two SSPs as decision rules for lot disposition have gained significant attention due to their superior performance. Depending on the switching mechanism for decision rules, acceptance sampling systems can be categorized into quick switching systems and two‐plan sampling systems (TSS), where TSS exhibits greater flexibility and adaptability in its rule‐switching mechanism. In this study, we construct a TSS with a sample size adjustment mechanism and integrate it with a third‐generation process capability index. Detailed investigation and analysis reveal that the proposed method provides more substantial incentives for suppliers, as its properties penalize suppliers who submit poor‐quality lots through increased sample size while rewarding suppliers who submit high‐quality lots by requiring smaller sample sizes. Finally, we demonstrate the application of the proposed method through a practical case study.

ABSTRACT We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific ‘sparsity’ constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artificial optimal design problem that can be solved using any existing mathematical programming technique for univariate‐response optimal designs under pure linear constraints. The solution to this artificial problem can then be directly converted into an optimal design for the primary multivariate‐response setting with combined linear and sparsity constraints. We demonstrate the utility and flexibility of the approach through a dose‐response case study with multivariate responses that sequentially adds constraints on safety, efficacy, and cost, where cost also depends on the number of distinct doses used.