Copula Model Research Articles

Spatial and temporal patterns of urban air pollution in tehran with a focus on PM2.5 and associated pollutants

Understanding the spatial and temporal dynamics of air pollutants is crucial for effective urban air pollution management. This study focuses on the temporal dynamics of air quality monitoring stations (AQMSs) and the association among air pollutants, particularly PM2.5, in Tehran, Iran. Using time series clustering and the Copula model, we analyzed data from 2019 to 2022. We found that the levels and dynamics of O3 and SO2 were similar across most AQMSs and unrelated to geographical positions. CO levels and dynamics were consistent among urban and border AQMSs, with higher concentrations in urban stations. NO2 levels and dynamics varied significantly among northern AQMSs with no relationship geographical positions. PM10 levels and dynamics had a relationship with geographical positions, with western clusters having the highest and northern clusters the lowest concentrations. The dynamics of PM2.5 showed significant relationship among AQMSs in the eastern, southern, and western regions, but not in the north. We also observed that PM10 and O3 levels were higher in warm seasons, whereas CO, SO2, NO2, and PM2.5 levels were higher in cold seasons. Most pollutants, except O3, peaked during traffic hours. Notably, the significant increase in PM2.5 since spring 2021 was primarily due to PM10. Policymakers should focus on these spatial and temporal variations to improve urban air quality and public health outcomes through targeted interventions.

Functional Principal Component Analysis for Continuous Non-Gaussian, Truncated, and Discrete Functional Data.

Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous scale), pain levels (truncated scale), mood states (ordinal scale), and the occurrence of daily life events (binary scale). These assessments, when indexed by time of day, can be treated and analyzed as functional data corresponding to their respective types: continuous, truncated, ordinal, and binary. Motivated by these examples, we develop a functional principal component analysis that deals with all four types of functional data in a unified manner. It employs a semiparametric Gaussian copula model, assuming a generalized latent non-paranormal process as the underlying generating mechanism for these four types of functional data. We specify latent temporal dependence using a covariance estimated through Kendall's bridging method, incorporating smoothness in the bridging process. The approach is then extended with methods for handling both dense and sparse sampling designs, calculating subject-specific latent representations of observed data, latent principal components and principal component scores. Simulation studies demonstrate the method's competitive performance under both dense and sparse sampling designs. The method is applied to data from 497 participants in the National Institute of Mental Health Family Study of Mood Spectrum Disorders to characterize differences in within-day temporal patterns of mood in individuals with the major mood disorder subtypes, including Major Depressive Disorder and Type 1 and 2 Bipolar Disorder. Software implementation of the proposed method is provided in an R-package.

Electricity supply research for ensuring food security in North China during droughts and floods: copula modeling for the water-energy-food nexus

Electricity supply research for ensuring food security in North China during droughts and floods: copula modeling for the water-energy-food nexus

Modeling extreme events: Univariate and multivariate data-driven approaches

AbstractThis article summarizes the contribution of team genEVA to the EVA (2023) Conference Data Challenge. The challenge comprises four individual tasks, with two focused on univariate extremes and two related to multivariate extremes. In the first univariate assignment, we estimate a conditional extremal quantile using a quantile regression approach with neural networks. For the second, we develop a fine-tuning procedure for improved extremal quantile estimation with a given conservative loss function. In the first multivariate sub-challenge, we approximate the data-generating process with a copula model. In the remaining task, we use clustering to separate a high-dimensional problem into approximately independent components. Overall, competitive results were achieved for all challenges, and our approaches for the univariate tasks yielded the most accurate quantile estimates in the competition.

Football competition risk early warning method based on improved Copula model

Football competition risk early warning method based on improved Copula model

MODELING THE BENEFITS OF A MARRIAGE REVERSE ANNUITY CONTRACT WITH DEPENDENCY ASSUMPTIONS USING ARCHIMEDEAN COPULA

Social security benefits may not be enough for retirement. Equity release products like marriage reverse annuities can boost retirement income for older couples. Marriage reverse annuity’s contract convert all or part of the real estate value of elderly spouses while they are living (joint life status) or after one partner dies (last survivor status). Since husband and wife face the same death risk, the chance of death between spouses is believed to be dependent for realism. Thus, copula models the future dependency model of a husband and wife. Sklar's theorem states that copulas link bivariate distribution and marginal cumulative functions. One of the most common copulas is Archimedean copula. Clayton, Gumbel, and Frank are Archimedean copula that will be used in this investigation. The Indonesian Mortality Table IV data is used to obtain the marginal distribution of the male and female which will then be used to construct copulas (Clayton, Gumbel, and Frank) that combine two marginal distributions into a joint distribution. The marginal distribution of Indonesian Mortality Table IV is uncertain, hence Canonical Maximum Likelihood parameter estimation is utilized to estimate the parameter of copulas. Multiple-state models depict the marriage reverse annuity model for joint life and last survivor status. The probability structure is based on Sklar's theorem and copula survival function. The contract benefits calculation utilizing copulas (Clayton, Gumbel, and Frank) shows that joint life status benefits are higher than last survivor status. Joint life status uses the dependence assumption with Frank's copula to calculate the smallest annual benefit value of a marriage reverse annuity contract, while last survivor status uses the independence assumption (without copula).

Research on Credit Risk Contagion of Commercial Banks Based on Copula Model

Research on the credit risk contagion effect of commercial banks is a key issue in credit risk management of commercial banks. This paper constructs a measurement framework for the credit risk contagion effect of commercial banks based on the Copula function theory. On the basis of selecting the appropriate Copula function and measuring specific parameters, taking Bank of China and Industrial and Commercial Bank of China as examples, the tail correlation coefficient was used to measure the credit risk contagion effect of the two banks, and relevant conclusions were drawn.

Separation of music signal spectrograms using copula models

The focus of this paper is on utilizing a copula-based technique for separating music signals. In this method, copulas are utilized to model the dependency structure of the source components. The objective is to minimize the Kullback-Leibler divergence between the copula density of the estimated source components and the copula density of the source components, which is assumed to be unknown. We give an application for the separation of stereo music recording using different copula models. We show through this application that by modeling the dependency between music signals, we can gain insights into the underlying structure of music signals and also we can ameliorate the separation performance.

Dynamic correlation between hog futures and industry chain: an empirical study based on time-varying copula model

Dynamic correlation between hog futures and industry chain: an empirical study based on time-varying copula model

Enhancing Drought Risk Assessment in the Punjab, Pakistan: A Copula-Based Modeling Approach for Future Projections

Abstract Drought is one of the most complicated and challenging natural hazards, which occurs nearly in every part of the world and poses recurring challenges to agriculture, food security, livestock, human health, and water management. Pakistan has a long history of drought; however, this study focuses on drought analysis and projection in the province of Punjab, Pakistan, as it provides around 60% of the country’s food product, significantly contributing to the national food supply and economy. This study utilized the previous 56 years (1962–2017) of climate data to calculate the reconnaissance drought index (RDI) and then extracted the drought variables of durations and severity for each meteorological station. The best-fit marginal probability distribution and copula models were chosen for the stations based on numerical as well as graphical evaluation. Lognormal and exponential probability distributions, as well as Gumbel, are selected as the best-fit probability distributions for both drought characteristics and bivariate copula model, respectively, for projections. From the projections, we can infer that the smaller return periods indicate high vulnerability while longer return periods with low vulnerability. The results suggest that Faisalabad, Bahawalpur, Bahawalnagar, and Multan stations have the lowest return periods, indicating high vulnerability, and may experience drought more frequently in the future. Mianwali, Khanpur, Lahore, and Sialkot stations may have an intermediate vulnerability to drought events. The stations of Jhelum, Murree, and Sargodha have larger return periods, implying lower susceptibility to drought events in the future. The projected results provide insights for policymakers and stakeholders to optimize the risk of droughts on agriculture production, livestock, water management, human health, and food security in Punjab, Pakistan.

Optimal scheduling strategy of household electrical equipment based on scenario dynamic modeling

Household electricity is highly unpredictable, necessitating a deep understanding of its impact on energy scheduling for optimal resource allocation and economic gains. This issue’s complexity can lead traditional optimization methods to converge on suboptimal solutions. In this study, the dynamic Copula (DC) model is used to construct the dynamic correlation between power consumption characteristics, and the Monte Carlo (MC) method is used to generate multiple power consumption scenarios to cope with the uncertainty of user behavior. Then, the optimal scenario set is selected through the average distribution error (ADE) to participate in the subsequent scheduling. In addition, based on the established equipment operation characteristic model, the electricity cost and load peak-to-average ratio (PAR) are comprehensively considered. The Improved Dynamic search multi-objective particle swarm optimization (IDSMOPSO) is introduced to optimize the running time of the equipment. Taking the electricity consumption of a family in Xi’an as an example, the results show that the algorithm is significantly better than the other two improved algorithms in performance. Meanwhile, the electricity cost of the family was significantly reduced by 17.09 %, and the PAR value was also reduced by 31.59 %, which realized the economic operation of household electricity.

A probabilistic framework for offshore aquaculture suitability assessment using bivariate copulas

Aquaculture at sea is gaining increasing importance, not only as a (local) food source but also due to its potential of being combined with other offshore activities such as wind parks. Nevertheless, experience of offshore aquaculture is limited. This study aims to provide a framework to evaluate offshore aquaculture suitability accounting for the probabilistic dependence between relevant variables. This framework is applied to obtain suitability maps of aquaculture for the North Sea for the blue mussel Mytilus edulis and the sugar kelp Saccharina latissima. For each of these species, three ecological variables are selected and the optimal growth and critical survival limits are defined. Here, suitability is defined as the probability of meeting these conditions. Data on the selected variables is extracted from a large-scale 3D hydrodynamic and ecological model of the northwest European Shelf, of which daily extremes are sampled. The probabilistic model is developed using bivariate copula models, which are fitted to each variable pair to describe their joint distribution function at each studied location. Empirical distribution functions are used to describe the univariate distribution function of each variable and location. Using Monte-Carlo simulations, the probability of meeting the optimal and critical limits is estimated and suitability maps accounting for the probabilistic dependence between the variables are generated. In addition, suitability maps disregarding the dependence are generated and compared to those accounting for the probabilistic dependence. It was found that considering the dependence between variables significantly improves the accuracy of the results for optimal and critical growth conditions for both species. The presented method allows to identify potential areas where blue mussel and sugar kelp cultivation is the most suitable. For instance, in this study, a north-south elongated area west of the German and Danish coast appears to be most suitable for blue mussels, while estuaries and rivers are found the most suitable for the sugar kelp.

Dependence Modeling for Tsunami and Earthquake Disasters in the Indonesian Megathrust Zones using Copula Models

The megathrust earthquake parameters that are related to the number of tsunami disasters (𝑍) are the number of earthquakes (𝑋) and the maximum earthquake magnitude (𝑌). The dependence property of these three random variables is stochastic due to the uncertainty of each event. This study provides the stochastic dependence model of (𝑋, 𝑍) and (𝑌, 𝑍) based on the historical data of tsunami and megathrust earthquake disasters occurring from 1905 to 2022 in five megathrust zones of Indonesia, namely the Sumatra, Java, Bali, Sulawesi and Papua zones. In this study, the stochastic dependence models applied are bivariate Copula models that are flexible under rigid assumptions. The data source is taken from the U.S. Geological Survey catalog. The results show that each megathrust zone has various responses to the earthquake and tsunami mechanisms; it can be seen from the probability functions of three random variables in each megathrust zone that they are significantly different. Furthermore, according to stochastic dependence modeling results, it is found that the Copula model selected for each zone varies in type and parameters. Moreover, the selected bivariate Copula models for each megathrust zone have better agreement with the data modeled than the conventional bivariate discrete models.

Some bivariate Schur-constant distributions and application to life insurance

Schur-constant models play a particular role when modelling time in fields such as actuarial science, insurance, reliability and survival models. These models describe random lifetimes with a certain dependence. In this study, a relation between proportional hazard rate distributions and Schur-constant models is established. Bivariate Schur-constant models, whose marginals are proportional hazard rate distributed, are introduced. Then, the dependency analysis in life insurances is performed through Schur-constant and copula models. It is revealed that there are differences in pricing when individuals' future lifetimes are dependent.

Enhancing the flexibility and power of adaptive seamless phase 2/3 design with copula modeling between short-term and long-term endpoints

Adaptive designs have garnered widespread attention in drug discovery studies as they are often more flexible, efficient, informative, and ethical. However, the planning of oncology trials with seamless phase 2/3 design is not as commonplace, especially when the primary endpoint involves time-to-event survival time and is expected to be immature at the interim for the purpose of treatment selection of the most-promising regimen. In this article, we establish a seamless phase 2/3 design with a review of the framework and adaptation to survival analysis, incorporation of treatment selection scheme guided by surrogate short-term endpoint at interim analysis, and integration of copula modeling for endpoints. We also explore parametric copula estimation using historical data, and investigate mis-specification among copulas families as well as against a straightforward family of the stratified model. For illustration, we provide extensive simulation with operating characteristics. The article concludes with a discussion of practical issues in the implementation of such designs.

Point cloud data-driven modelling of high-strength steel wire corrosion pits considering orientation features

We propose a corrosion pit modelling approach of high-strength steel wires considering orientation features using surface point cloud data, collected by three-dimensional laser scanning. Corrosion pits were identified through density-based spatial clustering of applications with noise (DBSCAN). The identified corrosion pits could be modelled as a semiellipsoid considering orientation features. The Gaussian copula model was utilised to describe the joint distribution of the geometric parameters of the corrosion pits. This approach will be valuable for simulation of the surface morphology of corroded high-strength steel wires.

Impact of COVID‐19 pandemic on the dependence structure and risk spillovers in global stock markets

AbstractThis study employs the MS‐GARCH‐EVT‐vine copula model to examine changes in the dependence structure and risk spillovers among global stock markets during the COVID‐19 pandemic. Our results indicate that the dependence structure of global stock markets exhibits intercontinental clustering characteristics. Specifically, the Hong Kong, French and US stock markets serve as the central nodes in the Asia‐Pacific, European and American regions, respectively. Furthermore, the COVID‐19 pandemic has reduced the number of stock markets directly linked to central nodes and exacerbated the synchronized decline in global stock markets. Additionally, the COVID‐19 pandemic has increased risk spillovers among global stock markets outside China, altering the direction of intercontinental risk contagion. These findings are significant for policy makers to prevent cross‐border risk spillovers and for investors to enhance their risk management strategies.

Quantile regression based on the counting process approach under dependent truncated data

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres.

A framework for drought monitoring and assessment from a drought propagation perspective under non-stationary environments

According to the coupled influence of climate variation and anthropogenic activities, hydro-meteorological variables are hard to keep stationary in a changing environment. Consequently, the efficacy of traditional standardized drought indices, predicated upon the assumption of stationarity, has been called into question. In China, the challenge of drought monitoring and declaration is exacerbated by the need for multiple drought indices covering meteorological, agricultural, hydrological, and groundwater aspects, often lacking real-time availability. To address these challenges, we developed a framework for drought monitoring and assessment from a drought propagation perspective. Central to this is the Nonstationary Integrated Drought Index (NIDI), which integrates responses from meteorological, agricultural, hydrological, and groundwater droughts, accounting for climate change and anthropogenic influences. First, we analyse the process of drought propagation to select the suitable time scale standardized drought index. Subsequently, significant large-scale climatic indices are selected through linear and nonlinear correlation analyses to identify climate anomalies. Anthropogenic influences are assessed using indicators such as the Normalized Difference Vegetation Index (NDVI), Impervious Surface Ratio (ISR), and population density (POP). Nonstationary probability models are then developed for precipitation, soil moisture, runoff, and groundwater series, incorporating climatic and human-induced factors. Finally, the NIDI is calculated using a D-vine copula model, with parameter estimation and updating facilitated by a genetic algorithm, representing the temporal dependence structure among the variables. A case study in the Hulu River Basin of western China validated the NIDI. Results showed that the NIDI effectively accounts for nonstationary hydro-meteorological variables due to climate change and human activities, accurately reproducing their time-dependent structure. Compared to conventional indices like SPI, SSI, SRI, and SGI, the NIDI identifies more extreme drought events. In conclusion, the presented NIDI offers a more comprehensive approach to drought identification, providing valuable insights for accurate drought detection and effective drought-related policy-making.

Synthetic data generation using Copula model and driving behavior analysis

In this study, the generation of synthetic driving data that can reflect real behavior well using the Copula model was investigated. To see the difference in behavior patterns in the generated synthetic driving data, a feature correlation comparison was made. The difference in driving behavior was provided with the K-means based classification model. It was shown that with a Random Forest model trained with synthetic data and having high accuracy, the privacy of real data could be protected by 98.55%. At the end of the study, it was seen that the Copula model could obtain synthetic driving data with sufficient accuracy with CAN bus data without additional sensor support.