Copula Method Research Articles

An analytical two-stage risk analysis model in the real-time reservoir operation

Flood risk analysis is vital for real-time reservoir operation. The reservoir operation horizon (OH) is generally longer than the streamflow forecast horizon (FH), while the gap between the FH and the OH was seldom considered in analytical flood risk models. This study develops an analytical two-stage risk model covering the period within the FH (the first stage) and from the FH to the OH (the second stage). In the first stage, the errors in forecasted streamflow and reservoir water level-storage relationships are considered using the multinormal distribution within the FH. In the second stage, design flood hydrographs are used to estimate the flood risk by conducting reservoir routing. Finally, the total flood risk is calculated by using the copula method to combine the flood risks from the first and second stages. Results for a case study using China’s Three Gorges Reservoir indicate that an effective FH can be identified to minimize flood risk, and balance between the forecast accuracy and length of the horizon. The length of the effective FH is not fixed and depends on reservoir inflow. Moreover, larger errors will not always lead to greater flood risks. The proposed method provides useful information on flood risk for real-time reservoir operation.

Analyzing risk contagion and volatility spillover across multi-market capital flow using EVT theory and C-vine Copula

There exists a potential interdependence among the United States markets, alongside an exceptional dependence on the East Asian stock markets. This transmission of risks is similarly evident in funds that are traded within markets. The current study seeks to uncover the pathways of risk contagion among various financial markets. This study examines how risks of funds spread across borders among China, the United States, and East Asia using Extreme Value Theory (EVT) and C vine copula quantile regression. It uses models such as AR (1), EGARCH (1, 1), Peak over Threshold (POT), and Copula methods to predict volatility events and correlation patterns during times of high volatility versus regular periods. Notably, the United States exhibits a risk transmission effect on the East Asian market compared to China. Furthermore, the findings indicate that, in times of high volatility, the risk spillover effect is comparatively weak, which is contrary to the situation of the US market. The study suggests that China's financial impact could progressively rise due to initiatives aimed at sector integration and enhancing financial independence. These findings have enlightening consequences for macro-prudential regulatory agencies, emphasizing the necessity of effective regulation to address cross-border risk spillovers. International investors can benefit from these results by incorporating risk-hedging strategies, accurately evaluating derivatives, and making wise investment decisions.

Multivariate stochastic generation of meteorological data for building simulation through interdependent meteorological processes

In recent years, the uncertainty of weather conditions and the impact of future climate change on building energy assessment has received increasing attention. As an important part of these studies, several types of methods for generating stochastic meteorological data have also been developed. Since solar radiation drops to zero at night, unlike the continuous 24-hour data for elements such as temperature and humidity, this has posed challenges for previous research to fully account for the simultaneity among multiple elements. Therefore, this study proposes a framework for meteorological data generation: First, perform multivariate time series modeling of meteorological data of air temperature, solar radiation and absolute humidity at 12:00 of each day of a typical year based on the S-vine copula method and simulating daily series data at 12:00 for 365 days. Then, based on the probability of change of each element evaluated from the historical meteorological observation data, the daily series data at 12:00 were expanded to 24 h, after which the yearly stochastic weather data were obtained. The analysis of 30 years of stochastic data generated by this method, compared with the original data, reveals that air temperature and solar radiation closely match the original distribution characteristics, except for a minor deviation in the absolute humidity’s kurtosis. Furthermore, the comparison of thermal load distributions for office buildings shows that the original data curve falls within the range of the generated data. This suggests that the generated data includes more information about uncertainty but still keeps the original data’s characteristics.

Coupled Effects of High Temperatures and Droughts on Forest Fires in Northeast China

High temperatures and droughts are two natural disasters that cause forest fires. During climate change, the frequent occurrence of high temperatures, droughts, and their coupled effects significantly increase the forest fire risk. To reveal the seasonal and spatial differences in the coupled effects of high temperatures and droughts on forest fires, this study used the Copula method and proposed the compound extremely high-temperature and drought event index (CTDI). The results indicated that the study area was subject to frequent forest fires in spring (71.56%), and the burned areas were mainly located in forests (40.83%) and the transition zone between farmland and forests (36.91%). The probability of forest fires in summer increased with high temperatures and drought intensity, with high temperatures playing a dominant role. The highest forest fire hazard occurred in summer (>0.98). The probability of a forest fire occurring under extreme meteorological conditions in summer and fall was more than twice as high as that in the same zone under non-extreme conditions. Droughts play a significant role in the occurrence and spread of forest fires during fall. These results can provide decision-making support for forest fire warnings and fire fighting in the Northeast China forest zone.

Prediction of long-term photovoltaic power generation in the context of climate change

Accurate long-term prediction of power generation in photovoltaic (PV) power stations is crucial for preparing generation plans and future planning. Quantitative prediction of future power generation from PV stations not only contributes to the stable operation of the local power system but also assists managers in formulating regional energy policies to promote renewable energy consumption. We utilized the NEX-GDDP-CMIP6 high-resolution climate dataset and employed the Vine Copula method for post-downscaling. This approach enabled high-resolution forecasts of key meteorological factors under different shared socioeconomic pathways (SSPs) scenarios (SSP245 and SSP585) for a PV power station in Yunnan, China. Additionally, we developed the KM-PSO-SVR power generation prediction model, which enables future accurate long-term PV power generation prediction. The results show that the Vine Copula multi-model ensemble downscaling model can effectively simulate the changes in key meteorological factors in the PV power station area. The KM-PSO-SVR model exhibited good simulation performance, with a mean absolute error of 0.843, root mean square error of 1.136, and correlation coefficient of 0.874 during the validation period. The results indicate that during the decade spanning from January 1, 2025, to December 31, 2034, radiation and wind speed will be decrease, while the temperature is expected to increase. In the SSP245 scenario, there is a 1.585 % increase in the average annual power generation during the future carbon peaking period (2025–2034). However, the SSP585 scenario, representing higher future emissions, shows a lower increase of 1.479 %.

ANALYSIS OF THE DEPENDENCIES COMMODITY PRICES AND STOCK MARKET INDEXES USING COPULA

Indonesia is rich in natural resources and occupies an important position in the global raw materials market. The country's rich resources such as oil, coal, nickel, and crude palm oil (CPO) have a significant impact on the economic situation. As one of the world's leading producers and exporters of these raw materials, Indonesia's economic fate is closely linked to price fluctuations. This study uses the copula method to model the dependence between stock and commodity returns and calculates the dependence between commodity prices (oil, coal, nickel, CPO) and Indonesian stock market index (IHSG) The data used for this analysis was sourced from Bloomberg.com, covering the period from 29 September 2021 to 29 September 2023. This study investigates the dynamic dependencies between commodity price returns and the Indonesian stock market index. The results show that the correlations between oil prices and the Indonesian stock index, and between CPO prices and the stock index are generally weak. However, there are exceptions to stock index returns, such as their relatively high dependence on coal and nickel. This diverse research provides valuable insight into the complex interdependencies in Indonesia's financial landscape. Understanding dependence between commodity prices and stock indexes is of great value to investors and policymakers, as it is the basis for making informed decisions to navigate the complex global economy.

VALUE AT RISK ESTIMATION FOR STOCK PORTFOLIO USING THE ARCHIMEDEAN COPULA APPROACH

Investment is one of the many ways to achieve future profits. One form of investment that is widely made is stocks. The return obtained in investing in stocks is potentially higher than other investment alternatives, but the risks borne are amplified, so it is necessary to analyze these risks that may occur. In this study, the Archimedean copula method is used to estimate the Value at Risk on shares of PT Bank Rakyat Indonesia Tbk (BBRI) and PT Telekomunikasi Indonesia Tbk (TLKM) for the period September 1, 2021, to August 31, 2023. The stock data is used to determine the Archimedean copula model and calculate the estimated value of Value at Risk (VaR) on the stock return portfolio using the Archimedean copula approach. The Archimedean copula models used are the Clayton copula model, Gumbel copula, and Frank copula. Of the three Archimedean copula models, the best model was selected by looking at the largest Maximum Likelihood Estimation (MLE) value. In this study, the log-likelihood value of Clayton copula is 7.958, Gumbel copula is 6.663, and Frank copula is 8.398. Therefore, Frank copula is the best Archimedean copula model with the largest log-likelihood value of 8.398 for the said data. Then the VaR estimation is done with the Frank copula model. The Value at Risk estimation results based on the Frank copula model show maximum loss rates of -0.0277 at the 90% confidence level, -0.0363 at the 95% confidence level, and -0.0516 at the 99% confidence level.

Climatic Challenges in the Growth Cycle of Winter Wheat in the Huang-Huai-Hai Plain: New Perspectives on High-Temperature–Drought and Low-Temperature–Drought Compound Events

Global climate change increasingly impacts agroecosystems, particularly through high-temperature–drought and low-temperature–drought compound events. This study uses ground meteorological and remote sensing data and employs geostatistics, random forest models, and copula methods to analyze the spatial and temporal distribution of these events and their impact on winter wheat in the Huang-Huai-Hai Plain from 1982 to 2020. High-temperature–drought events increased in frequency and expanded from north to south, with about 40% of observation stations recording such events from 2001 to 2020. In contrast, low-temperature–drought events decreased in frequency, affecting up to 80% of stations, but with lower frequency than high-temperature–drought events. Sensitivity analyses show winter wheat is most responsive to maximum and minimum temperature changes, with significant correlations to drought and temperature extremes. Copula analysis indicates temperature extremes and drought severity are crucial in determining compound event probability and return periods. High-temperature–drought events are likely under high temperatures and mild drought, while low-temperature–drought events are more common under low temperatures and mild drought. These findings highlight the need for effective agricultural adaptation strategies to mitigate future climate change impacts.

Parameter estimation of grouting pressure and surface subsidence on the reliability of shield tunnel excavation under incomplete probability information

Most of the results obtained from traditional tunnel reliability models are based on conclusions of deterministic parameters, and ignoring the correlation between parameters tends to generate unreliable conclusions for the analysis. This study investigated the influence of grouting pressure and surface subsidence on the reliability of shield tunnel excavation considering the dependency structures between parameters. A probabilistic analysis approach based on copula method is applied to evaluate the bivariate dependency structure. Firstly, 88 sets of measured data are selected from various tunnel projects at home and abroad, and their statistical parameters and marginal distribution functions are determined. Secondly, a bivariate joint probability distribution model of shield grouting excavation is established, and Monte Carlo Simulation is applied to explore the influence of the selection of the copula function on the failure probability of the shield grouting excavation. The results indicate that under incomplete probabilistic information, disregarding the negative correlation between the parameters will underestimate the reliability of shield grouting construction and yield an overly conservative reliability design. Subsequently, varying the magnitude of the parameter limit values to explore the effect on the failure probability will be advantageous for reliability analysis in dynamic construction. Finally, by varying the sample size of the simulation and original measured data, it is found that excessively small simulated and original sample sizes can lead to inaccurate reliability assessment.

On the Ratio-Type Family of Copulas

Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form uv/(1−θf(u)g(v)). It includes numerous examples and discusses the admissible range of parameter θ, showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, uv/(1−θϕ(u,v)), and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ-inversion, and the moment copula method.

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment.

The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators.

Did Precious Metals Serve as Hedge and Safe-haven Alternatives to Equity During the COVID-19 Pandemic: New Insights Using a Copula-based Approach

We examine the hedging and safe-haven characteristics of gold, silver, platinum, and palladium and three major indices in the US market. The metal markets are known for their hedging characteristics during financial distress. This article sheds new insights using high-frequency data into precious metals’ hedging and safe-haven abilities under extreme market volatility conditions attributed to the COVID-19 crisis using the copula method. The results show that gold outperforms all other precious metals in hedging and as a safe haven under extreme stock market conditions, in both the pre-crisis and crisis periods, with silver as the next best alternative. JEL codes: G01, G11, G15, G19

Skillful seasonal prediction of the 2022–23 mega soil drought over the Yangtze River basin by combining dynamical climate prediction and copula analysis

An unprecedented soil moisture drought broke out over the Yangtze River basin (YRB) in the summer of 2022 and lasted until the spring of 2023, caused great economic losses and serious environmental issues. With the rapid onset and long-lasting duration, the mega soil drought challenges the current seasonal prediction capacity. Whether the state-of-the-art climate models provide skillful predictions of the onset, persistence and recovery of the 2022–23 mega soil drought needs to be assessed. Identified by the drought area percentage, here we show that the mega soil drought over the YRB started from July, 2022, reached the peak in August, and diminished in April, 2023. Combined with real-time predictions of monthly precipitation released by three climate models participating in the North American multi-model ensemble (NMME) project, we predict the monthly evolution of the 2022–23 soil drought through a joint distribution between precipitation and soil moisture established by the copula method. The results indicate that the NMME/copula prediction well reproduced the spatiotemporal evolution of the mega soil drought at 1 month lead. Using the climatological prediction that relies on the information of initial soil moisture conditions as the reference forecast, the Brier skill score (BSS) values for NMME multi-model ensemble are 0.26, 0.23 and 0.2 for the forecast lead times increased from 1 to 3 months during the entire soil drought period. Specifically, the BSS is 0.14 at 2 months lead during drought onset stage, and 0.26 at 3 months lead during persistence stage, while it is close to zero at all leads during the recovery stage. Our study implies that climate models have great potential in probabilistic seasonal prediction of the onset and persistency of mega soil drought through combining with the copula method.

Copula deep learning control chart for multivariate zero inflated count response variables

With the increasing popularity of big data analysis, research on zero-inflated count data with the copula method has garnered significant attention because zero-inflated count data do not follow a normal distribution and have high correlation among variables. Within the domain of quality control, there has been limited emphasis on multivariate statistical process control (SPC) techniques that specifically address the challenge of multicollinearity within regression models for multivariate zero-inflated count responses. In this paper, we explain a computational challenge in handling big data with parametric generalized linear models, such as the zero-inflated Poisson model. This challenge motivates us to introduce a copula-based deep learning and neural network model involving multivariate zero-inflated count response variables with highly correlated explanatory variables. This approach builds upon existing deep learning and neural network models designed for univariate count responses, expanding them to encompass multivariate count response models through the integration of a copula regression framework. To evaluate the performance of our proposed methodology, we conduct a comparative analysis of accuracies using the zero-inflated Poisson model, univariate deep learning and neural network models, multivariate count response deep learning and neural network models, and our proposed copula deep learning and neural network models. This assessment involves employing metrics such as root mean square error (RMSE), weighted mean absolute percentage error (WMAPE), and mean absolute deviation (MAD). We include both copula-based asymmetrical zero-inflated simulated data and real-world data. We also propose a temporal dependence control chart for assessing the temporal dependence between bivariate zero-inflated count response variables. Our proposed copula deep learning and neural network temporal control charts can check time-varying dependence and outliers by leveraging the Shewhart statistical process control chart and t-copula ARMA-GARCH dynamic control correlation.

A novel compound G family with properties, copulas, modelling the asymmetric and positive-skewed engineering and medical data

It is essential to use compound families in statistical modeling for asymmetric-positive-skewed reliability and relief in real-life data for a number of reasons, including the capacity to capture underlying patterns and characteristics in the data more accurately. The current work introduces a novel compound and continuous G family of probability distributions characterized by two parameters, denoted as the compounded two-parameters general Rayleigh geometric family of probabilistic distributions. The research involves rigorous calculations to ascertain and analyze the relevant mathematical properties of this newly proposed family. We present aging notions under the new family, providing corresponding density, hazard, and survival functions. Notably, a specific emphasis is placed on the examination of the reciprocal-Weibull baseline model, both from a mathematical and statistical perspective, in a dedicated section of the study. To generate various multivariate and bivariate type distributions, the copula method is employed. These newly derived models hold significant utility for effectively modeling the multivariate and bivariate data. The study showcases the wide applicability in different sides under real-life datasets. The presented applications serve as concrete demonstrations of the family's effectiveness and versatility in addressing real-world scenarios.

Relationship between fintech by Google search and bank stock return: a case study of Vietnam

Due to the ongoing global debate regarding the relationship between fintech and banks, including developing countries, this study aims to investigate this relationship in the case of Vietnam, an emerging nation. The study analyzes the relationship between fintech search and bank stock returns, which are measures of fintech and banks, respectively. The time series data for fintech and bank stock returns were obtained from Google Trends and Vietstock, respectively. Exploratory factor analysis was utilized to derive the fintech variables, while the bank stock return variable was calculated using a basket of eight listed banks from 2017w46 to 2021w46. The results were estimated using the vector autoregression and Granger causality method and validated with the copula method. A key finding of this study is the presence of a simultaneous negative change and bidirectional causality between bank stock returns and fintech lending. Furthermore, several other interesting findings were discovered: (1) the causal relationship from fintech to bank stock returns is weaker compared with the opposite direction; (2) unidirectional causality exists between different types of fintech, such as influence from FinFintech to FinLending, from FinPayment to FinLending and FinWallet, from FinMoney to FinFintech, from FinWallet to FinLending, and from FinProduct to FinFintech; and (3) there is an equal occurrence of simultaneous increase or decrease between bank stock returns and certain types of fintech, specifically between BankReturn and FinPayment, BankReturn and FinLending, as well as BankReturn and FinWallet. These findings shed light on the complex relationship between fintech and banks, offering insights that contribute to our understanding of this dynamic interplay in the context of Vietnam’s emerging fintech landscape.

Flash flood detection via copula-based intensity–duration–frequency curves: evidence from Jamaica

Abstract. Extreme rainfall events frequently cause hazardous floods in many parts of the world. With growing human exposure to floods, studying conditions that trigger floods is imperative. Flash floods, in particular, require well-defined models for the timely warning of the population at risk. Intensity–duration–frequency (IDF) curves are a common way to characterize rainfall and flood events. Here, the copula method is employed to model the dependence between the intensity and duration of rainfall events flexibly and separately from their respective marginal distribution. Information about the localization of 93 flash floods in Jamaica was gathered and linked to remote-sensing rainfall data, and additional data on location-specific yearly maximum rainfall events were constructed. The estimated normal copula has Weibull and generalized extreme value (GEV) marginals for duration and intensity, respectively. Due to the two samples, it is possible to pin down above which line in the intensity duration space a rainfall event likely triggers a flash flood. The parametric IDF curve with an associated return period of 216 years is determined as the optimal threshold for flash flood event classification. This methodology delivers a flexible approach to generating rainfall IDF curves that can directly be used to assess flash flood risk.

Analysing spatio-temporal drought characteristics and copula-based return period in Indian Gangetic Basin (1901-2021).

Uncertainty and uneven distribution of monsoonal rainfall and its consequences on crop production is a matter of serious concern in India, specifically, in theIndo-Gangetic plainregion. In this study, drought patterns were investigated through standardised precipitation index (SPI) of varying timescales, using the India Meteorological Department (IMD) precipitation data (1901-2021). We analysed the spatio-temporal pattern of different drought characteristics (frequency, duration, severity, intensity) of the Indian Gangetic basin using run theory. The bivariate copula method has been incorporated to combine two drought properties (severity and duration). Copula integrates multivariate distribution and considers the dependency rate among the variables. The five most widely used copulas from various copula families, elliptical (normal, t-copula) and Archimedean (Clayton, Gumbel, Frank), were estimated for modelling, and the best fit copula was selected. The study revealed that seasonal drought is more frequent and intense in the Upper and Middle Gangetic Plain, whereas annual drought is quite scattered in nature. It is worthy to mention that downward drought trends were observed in this agricultural belts significantly after 1965; specifically, in the Upper, Middle, and Trans Gangetic Plain regions. With increasing drought duration and severity, the drought return period raised, but the frequency decreased gradually. Most of the droughts characterised by less duration and severity occurred with a return period below 10years for the whole region. The major 100 + years return period droughts were to be found after 1960 and their frequencies were significantly higher after 2000. The most recent remarkable droughts with more than 100years of return occurred during 2008-2011 and 2016-2018 in the Upper and Middle Gangetic plains, whereas in the Lower Gangetic plain, a hundred-year return period drought was occurred during 2010-2013. This study provides agroclimatic-zones-wise significant information of drought characteristics and its nature of occurrence in the Indian Ganga Basin. The results enhance the understanding of drought management and formulation of adaptive strategies to mitigate the adverse impact of droughts.

Understanding drought propagation through coupling spatiotemporal features using vine copulas: A compound drought perspective

Accurately evaluating drought impact on agriculture poses a challenge to regional food security, particularly in compound drought (i.e., meteorological and agricultural drought co-occurring) scenarios. This study presents a novel approach utilizing Vine copula for coupling spatiotemporal features to evaluate drought propagation. Three-dimensional clustering method was employed to identify meteorological and agricultural drought events, which excelled in capturing dynamic evolution characteristics (duration, area, severity, etc.) as well as integrating them into comprehensive meteorological drought intensity (IMD) and agricultural drought intensity (IAD). Through spatiotemporal matching, compound drought events were extracted from the meteorological-agricultural drought event pairs. From compound drought perspective, compound duration (CD) and compound area (CA) were devised to characterize drought propagation potential across time and space. Finally, the Vine copula method was employed to model the interdependence between four key coupling features, namely IMD, IAD, CD, and CA, and evaluate the probability of triggering agricultural drought with different intensity levels. Results showed that CD and CA can respectively characterize the temporal and spatial accumulation scale of drought propagation. At a certain IMD level, CD significantly influences the propagation probability (i.e., “stratification” phenomenon), while CA increases the probability proportionally. Probability evaluation lacking spatiotemporal information may underestimate the likelihood of drought propagation characterized by “low-IMD” but “long-CD” or “large-CA”. The four-dimensional Vine copula structure can effectively couple dependence relationships of compound drought characteristics, and exhibits reliable robustness. This research provides stakeholders accurate probabilistic evaluation under compound drought scenarios, offering new insight into drought propagation.

A risk-aware and second-order cone programming model for wind expansion planning considering correlated uncertainties using the copula method

Integration of large-scale renewable energy sources (RESs) into existing power grids is challenging for power system operators and planners due to the intermittent and uncertain characteristics of RESs and the limitation of transmission capacity. This paper presents a new risk-based framework to obtain the optimal placement and sizing of wind farms in the bulk power system considering the impact of mutual correlation between wind farms’ power productions in different candidate buses. In this regard, a second-order cone programming (SOCP) optimization problem is developed to minimize the total expected social cost including the operation cost of conventional generators, wind curtailment cost, and the investment cost of newly installed wind farms. In the proposed model, the correlated uncertainties of wind power production are incorporated using the copula method. Also, the conditional value-at-risk (CVaR) measure is utilized to manage the risk of the model associated with uncertainties. The proposed planning model is then implemented into the Garver 6-bus and IEEE 118-bus test systems. Given the results, employing SOCP-based AC OPF in the presented planning model results in a precise solution, demonstrating an 87% reduction in running time. Moreover, the numerical results illustrate that by considering the correlation between wind farms’ power production and reducing the risk parameter, there is a significant increase in the installed capacity of wind farms.