Copula Method Research Articles

Analyzing spillover effects of selected cryptocurrencies on gold and brent crude oil under COVID-19 pandemic: Evidence from GJR-GARCH and EVT copula methods

This study examines the dependence structure and estimates the Value at Risk (VaR) and risk spillover between cryptocurrencies, oil, and Gold market data. In this paper, we estimate VaR by applying a hybrid approach of extreme value theory (EVT), copula functions, and GARCH models. We implement this method in a dual pair of selected data: the cryptocurrencies (Bitcoin and Ripple) and the Brent crude oil and gold markets. To estimate the VaR structure of these combinations, we initially employ asymmetric GARCH and EVT methods to model the marginal distributions of each return series and subsequently apply Copula functions (Gaussian, Student's t, Clayton, and Frank) to connect the marginal distributions into a multivariate distribution. Based on the results, we infer that, generally, the GARCH-EVT-Copula approach works well and is better than traditional methods (e.g., Historical Simulation (HS) and variance-covariance (VC)). These results show that the GARCH-EVT-Copula model is the best method for examining the dependence structure. Finally, we implement the technique of Diebold-Yilmaz to compute the spillover index between four data before and during the COVID-19 pandemic. From this part, we conclude that cryptocurrencies have spillovers on each other, but their spillovers on Gold and oil are very small. This phenomenon implies that cryptocurrencies are tough to hedge against other financial assets but are appropriate diversifiers in an investor's portfolio. The current study's findings benefit all investors and financial market professionals who want to learn about the cryptocurrency market as a new asset class or incorporate it into their investment strategies or portfolios.

Dynamic vulnerability assessment of maize under low temperature and drought concurrent stress in Songliao Plain

With global climate change, most parts of the world face more than one natural disaster. Field crops must cope with a combination of two or more stresses. System vulnerability has changed, and quantitative vulnerability analysis is imminent and challenging. Based on the crop water surplus deficit index (CWSDI) and low-temperature index (LTC), this study used the copula method to establish a dynamic assessment model of maize vulnerability under different low temperature and drought concurrent stress intensities, finally showed it in two forms of three-dimensional surface and spatial distribution, which was more vivid and comprehensive. The main conclusions are as follows: the peak number of individual events and concurrent events of low temperature and drought is significantly different, the time trend of the number of concurrent events in each growth period is not the same, and the interannual difference is significant; low-temperature severity and maize yield loss rate, low-temperature severity, and drought severity had significant correlation. Based on this, a 3 C-vine-copula model was established and passed the test. The interaction between the joint probability of concurrent event intensity and the loss rate leads to complex changes in vulnerability. When low temperature and drought are concurrent, the vulnerability analysis cannot be simply superimposed by low temperature and drought intensity. The vulnerability distribution of maize at different growth stages in Songliao Plain shows noticeable regional differences. The central and southern parts of the study area are the most vulnerable areas under low-temperature and drought stress. This study’s results can help managers adjust agricultural resources and adopt more effective irrigation policies under combined stress conditions.

Implementation of Bayesian Simulation for Earthquake Disaster Risk Analysis in Indonesia based on Gutenberg Richter Model and Copula Method

Indonesia is a country prone to earthquakes because it is located in the Pasific ring of fire area. The earthquakes caused a lot of damages and casualties. In this paper, we use Bayesian Simulation on Gutenberg Richter model and Copula method to estimate the risk parameters of earthquake, specifically the probability and the recurrence (return) period of an earthquake occurrence in Indonesia. Those risk parameters are estimated from dependence structure of frequency and magnitude of earthquakes. The dependence structure can be determined by using Gutenberg Richter model and Copula method. The Gutenberg Richter model is a model based on linear regression used to determine dependence structure, while the Copula method is a statistical method used to determine dependence structure that ignores linearity and normality assumptions of data. Bayesian Simulation is a method used to estimate parameters based on simulation. The data used is an annual data of frequency and magnitude (magnitude ≥ 4 Richter Scale) of earthquakes occur in Indonesia for 4 years from Meteorological, Climatological, and Geophysical Agency of Indonesia. There are several steps of analysis to be performed: firstly, we perform regression analysis of frequency and magnitude of the earthquakes to determine Gutenberg Richter Model; secondly, we perform Copula analysis; thirdly, we estimate probability and the recurrence (return) period of an earthquake occurrence using Bayesian Simulation based on the result of step one and two. The result indicates Bayesian Simulation can estimate risk parameters very well.

The Typhoon Wind Hazard Assessment Considering the Correlation among the Key Random Variables Using the Copula Method

The Typhoon Wind Hazard Assessment Considering the Correlation among the Key Random Variables Using the Copula Method

Stress testing bank insolvency risk by systemic equity market shock: An expected shortfall approach

This paper proposes a simple intuitive approach for assessing and stress testing the insolvency risk of global systemically important banks (G-SIBs) by shocking systemic risk in the equity market. In particular, the paper introduces two metrics to measure the relative adequacy of total loss absorbing capacity (TLAC) upon resolution of a bank under both real market conditions and stress test settings. The metrics may also be calculated on a regular basis for monitoring bank insolvency risk. Three global systemically important banks, including Credit Suisse, are presented as examples for the analysis. To capture the heavy tail feature of equity market downturns and ensure conservatism for stress testing, an analytical framework is adopted based on extreme value theory with expected shortfall, power law distributions and copula method. The analysis concludes that G-SIBs may have a high probability of loss exceeding TLAC under systemic market stress.

Maximum entropy copula for bivariate drought analysis

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model.

Unveiling commodities-financial markets intersections from a bibliometric perspective

The prominence of commodity markets within the domains of empirical finance and energy economics is well established, largely due to oil's importance and its relationship with other commodities and financial markets. In this study, we present a bibliometric examination of 437 journal articles addressing the phenomenon of commodity connectedness, spanning the period from 1994 to 2022. The research methods include a blend of qualitative and quantitative approaches, incorporating bibliometrics and content analysis. Based on the findings of the analysis, four primary research streams have been identified within the literature concerning commodity connectedness, namely (1) commodity interconnectivity, (2) the relationship between traditional commodities, renewable energy, and cryptocurrencies, (3) the relationship between oil and stock markets, and (4) studies utilizing copula methods to examine the interconnectivity between oil and financial markets. We proposed 15 future research questions for further investigation in the domain of commodity connectedness, including topics such as the impact of the post-COVID era and global uncertainties on commodity markets, how commodities can address the issue of climate change, the exponential growth of cryptocurrencies as a new financial asset, and the impact of the ongoing Russia-Ukraine conflict on commodity and financial markets.

Geostatistical Evaluation of a Porphyry Copper Deposit Using Copulas

Kriging has some problems such as ignoring sample values in giving weights to them, reducing dependence structure to a single covariance function, and facing negative confidence bounds. In view to these problems of kriging in this study to estimate Cu in the Iju porphyry Cu deposit in Iran, we used a convex linear combination of Archimedean copulas. To delineate the spatial dependence structure of Cu, the best Frank, Gumbel, and Clayton copula models were determined at different lags to fit with higher-order polynomials. The resulting Archimedean copulas were able to describe all kinds of spatial dependence structures, including asymmetric lower and upper tails. The copula and kriging methods were compared through a split-sample cross-validation test whereby the drill-hole data were divided into modeling and validation sets. The cross-validation showed better results for geostatistical estimation through copula than through kriging in terms of accuracy and precision. The mean of the validation set, which was 0.1218%, was estimated as 0.1278% and 0.1369% by the copula and kriging methods, respectively. The correlation coefficient between the estimated and measured values was higher for the copula method than for the kriging method. With 0.0143%2 and 0.0162%2 values, the mean square error was substantially smaller for copula than for kriging. A boxplot of the results demonstrated that the copula method was better in reproducing the Cu distribution and had fewer smoothing problems.

The oil price-macroeconomy dependence.

This paper investigates the relationship between the price of oil and real output in the United States in the context of a Markov regime switching, identified, structural GARCH-in-Mean VAR model with copulas. We use the copula method to investigate the nonlinear dependence structure, as well as (upper and lower) tail dependence, between the price of oil and real output growth, and Markov regime switching to account for changing oil price dynamics over the sample period. We find an asymmetric negative dependence structure between oil price and output growth shocks and that oil price uncertainty has a negative and statistically significant effect on real output growth.

Fatigue reliability analysis of floating offshore wind turbines considering the uncertainty due to finite sampling of load conditions

The fatigue reliability-based design is critical for the structural safety of floating offshore wind turbines (FOWTs). In principle, infinite potential load conditions that the FOWT may experience should be considered in fatigue assessment, while in practice only limited number of load conditions are used, which inevitably induces uncertainty to fatigue estimation. However, to this uncertainty, little attention has been paid. In this study, the fatigue reliability of a FOWT is investigated with a focus on this uncertainty. The C-vine copula method is adopted to model concurrent wind and wave conditions, and the probability-based sampling method is employed to determine the load conditions used for fatigue analysis. This uncertainty is assessed quantitatively via bootstrap method based on numerous simulations. The Gaussian random variable can be used to describe the uncertainty, and the standard variation is proportional to the −0.5 power of the number of load conditions. The fatigue reliability evaluation model of FOWT is established considering this uncertainty, and sensitivity analysis is performed to assess the influence of different random variables. The results indicate that the effect of this uncertainty is comparable to some other uncertainties in certain cases, and should be paid attention to in practice.

Efficient and Unbiased Safety Test for Autonomous Driving Systems

Test the safety of Autonomous Driving Systems (ADS) with realistic traffic conditions is important to the insurance industry, legislators, and third-party technical services. However, the scarcity of risky driving events distributed in real-world driving often makes sampling inefficient. In this paper, we propose a unified and hierarchical testing framework for efficient and unbiased safety tests of ADS. We first extract the risk subspace from the Naturalistic Driving Data (NDD) with defined safety measures. Subsequently, we use the Gaussian Copula method to accurately model the subspace joint probability density function (PDF). We further formulate a Kriging model-based optimization problem for finding the appropriate Importance Sampling (IS) parameters, where the Kriging model is trained iteratively within limited computational resources. Eventually, the risky concrete scenarios library is generated using the obtained Importance Sampling parameters. With the simulation results skewered back to the original risk subspace, the ADS probability of failure (e.g., crash rate) can thus be accurately and unbiasedly estimated. Experiment results show that using 0.94% computational resources, the Kriging surrogate model captures 96.04% of ADS crashes with at least 90.25% precision. On crash rate estimation, our proposed method achieves a consistent result with that of Monte Carlo simulation, provided that the relative error does not exceed 10% while improving the testing efficiency by up to 6,539 times.

Absolute intragenerational income mobility in Iran

Absolute intragenerational income mobility (AIIM), defined as the percentage of households with higher income compared to their previous year, is a complementary index to aggregate measures such as income per capita and the Gini index to show a more detailed picture of an economy. Panel data on household income is necessary to estimate AIIM, but it is not usually available in developing countries and, in the long run, for most developed countries. In this paper, we employ copula modeling and cross-sectional income data in a developing country, Iran, and well approximate the mobility estimated by panel data for the years 2011–2019 and then utilize the copula method to extend our estimation backward until 1991. Our findings reveal that absolute intragenerational income mobility in Iran for urban households fluctuates between 40 % and 62 %. AIIM is higher for low-income households.

Dependence structures among geopolitical risks, energy prices, and carbon emissions prices

This paper examines the short-, medium-, and long-run dependence structures for all distribution quantiles among carbon emissions prices, crude oil prices, natural gas prices, and geopolitical risks in Brazil, China, India, Russia, and South Africa from January 2003 to September 2019. The paper utilises the volatility spillover approach of Diebold-Yilmaz to identify the dependence structure among crude oil prices, natural gas prices, carbon emissions prices, and geopolitical risks within the variational mode decomposition-based copula method. It is observed that dependence structure across geopolitical risks and oil prices is time and frequency varying. It is also found that the dependence structure across geopolitical risks and oil prices is positive and valid at different periods and quantiles. The evidence has policy implications for hedging and portfolio risk diversification strategies and policymakers.

THE APPLICATION OF GUMBEL COPULA TO ESTIMATE VALUE AT RISK WITH BACKTESTING IN TELECOMMUNICATION STOCK

The Value at Risk (VaR) method refers to a statistical risk measurement tool used to determine the maximum loss of an investment, while the distribution that must be met is the normal distribution. This is not in line with the actual situation, because the distribution of the return value is found to be not normally distributed but depends on market conditions that occurred at that time, thus invalidating the VaR estimate and resulting in greater portfolio risk. Therefore, in this study, the estimation of risk value will be carried out using the Gumbel Copula method which can model the dependency structure between stocks and is flexible enough to model financial return data from https://finance.yahoo.com/. The parameter estimates produced by the Gumbel Copula method are then used to calculate the VaR at 90%, and 99% confidence levels. The resulting VaR values ​​are 0,076 and 0.231. To test the feasibility of the VaR model, backtesting was carried out and concluded that the VaR value obtained was valid and suitable for use in the risk assessment of PT. XL Axiata Tbk and PT. Telkomunikasi Indonesia Tbk.

Reliability modeling of weighted-k-out-of-n: G system under multiple failure modes with dependent components

In engineering practice, some weighted-k-out-of-n: G systems often show multiple performance levels, resulting in multi-failure-mode mechanism. For these complex degradation systems, a novel reliability model with heterogeneous components is proposed on account of the number of working components, the total weight, and the sojourn time in some a stage, where different weights and thresholds are taken into account in different stages, and so do failure modes. After presenting the indispensable definitions of first passage time and the system lifetime, the system reliability indexes are derived by the Copula method to depict the dependence between components. Furthermore, maximum likelihood estimation of the Copula parameters is adopted and a Copula-based expression for component importance in each type is obtained. Finally, the reliability of the overall supercharging subsystem of an advanced fighter air energy system, as an example of weighted-k-out-of-n: G system with multi-failure modes is analyzed by the suggested model, which offers the comparison of independent and dependent cases. Meanwhile, sensitivity analysis is available to point out the effects on the system.

Using copulas to enable causal inference from nonexperimental data: Tutorial and simulation studies.

Causal inference in psychological research is typically hampered by unobserved confounding. A copula-based method can be used to statistically control for this problem without the need for instruments or covariates, given relatively lenient distributional assumptions on independent variables and error terms. The current study aims to: (a) provide a user-friendly introduction to the copula method for psychology researchers, and (b) examine the degree of non-normality in the independent variables required for satisfactory performance. A Monte Carlo simulation study was used to assess the behavior of the copula method under various combinations of conditions (sample size, skewness of independent variables, effect size, and magnitude of confounding). In addition, an applied example from research on the effects of parental rearing on adult personality and life satisfaction was used to illustrate the method. Simulations revealed that the copula method performed better at higher levels of skewness in the independent variables, and that the impacts of lower skewness can be offset to some extent by larger sample size. When skewness and/or sample size is too small, the copula method is biased toward the uncorrected model. In the applied example, parental rejection/punishment predicted less adaptive personality and life satisfaction, with no evidence of confounding. For parental control/overprotection, there was evidence that confounding attenuated the estimated relationship with personality/life satisfaction. Copula adjustment is a promising method for handling unobserved confounding. The discussion focuses on how to proceed when assumptions are not quite met, and outlines potential avenues for future research. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Load condition determination for efficient fatigue analysis of floating offshore wind turbines using a GF-discrepancy-based point selection method

Fatigue failure is one of the decisive factors to be considered in the structural safety design of floating offshore wind turbines (FOWTs). In the fatigue assessment of FOWTs, adequate simulations are required to account for the variability of long-term environmental load conditions. Although the number of potential environmental conditions can be infinite, only a limited number of representative load conditions are used in practice. This inevitably introduces uncertainty into the fatigue estimation, which is usually referred to as the finite sampling-induced uncertainty. To reduce this uncertainty, numerous simulations are required at the expense of unbearable computation burdens. The present study proposes a method to determine the representative load conditions for efficient fatigue evaluation of FOWTs based on the GF-discrepancy of point set. The copula method is adopted to establish the joint probabilistic model of long-term wind and wave conditions. The in-house developed StoDRAFOWT model and the SN-curve approach are employed for the fatigue evaluation. The fatigue uncertainty due to finite sampling under different load condition selection methods is then assessed. The comparison results indicate that the proposed method can significantly reduce the uncertainty in the fatigue estimation of FOWTs against conventional methods, thus improving the fatigue analysis efficiency of FOWTs.

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring.

Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package "compound.Cox". The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

Assessment of the Joint Impact of Rainfall Characteristics on Urban Flooding and Resilience Using the Copula Method

Assessment of the Joint Impact of Rainfall Characteristics on Urban Flooding and Resilience Using the Copula Method

Linear Consecutive-k-out-of-n: G System Reliability Analysis

The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.