Uncovering hidden mixture correlation among variables have been investigating in the literature using mixture R-vine copula models. These models are hierarchical in nature. They provides a huge flexibility for modelling multivariate data. As the dimensions increases, the number of the model parameters that need to be estimated is increased dramatically, which becomes along with huge computational times and efforts. This situation becomes even much more harder and complicated in the mixture Regular vine models. Incorporating truncation method with mixture Regular vine models will reduce the computation difficulty for the mixture based models. In this paper, tree-by-tree estimation mixture model is joined with the truncation method, in order to reduce the computational time and the number of the parameters that need to be estimated in the mixture vine copula models. A simulation study and a real data applications illustrated the performance of the method. In addition, the real data applications show the affect of the mixture components on the truncation level.

This study generalized the best copula to characterize the joint probability distribution between rainfall severity and duration in Peninsular Malaysia using two dimensional copulas. Specifically, to construct copulas, Inference Function for Margins (IFM) and Canonical Maximum Likelihood (CML) methods were specially exploited. For the purpose of achieving copula fitting, the derived rainfall variables by making use of the Standardized Precipitation Index (SPI) were fitted into several distributions. Five copulas, namely Gaussian, Clayton, Frank, Joe and Gumbel were put to the tests to establish the best data fitted copula. The tests produced acknowledged and satisfactory results of copula fitting for rainfall severity and duration. Surveying the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), only three copulas produced a better fit for parametric and semi parametric approaches. Finally, two consistency tests were conducted and the results had shown that Frank Copula produced consistent results.

Especially for drought periods, the higher the accuracy of reservoir inflow forecasting, the more reliable the water supply from a dam. The article focuses on probabilistic forecasting of seasonal inflow to reservoirs and determines estimates from the probabilistic seasonal inflow according to drought forecast results. The probabilistic seasonal inflow was forecasted by a copula-based Bayesian network employing a Gaussian copula function. Drought forecasting was performed by calculation of the standardized streamflow index value. The calendar year is divided into four seasons; the total inflow volume of water to a reservoir for a season is referred to as the seasonal inflow. Seasonal inflow forecasting curves conforming to drought stages produce estimates of probabilistic seasonal inflow according to the drought forecast results. The forecasted estimates of seasonal inflow were calculated by using the inflow records of Soyanggang and Andong dams in the Republic of Korea. Under the threshold probability of drought occurrence ranging from 50 to 55 %, the forecasted seasonal inflows reasonably matched critical drought records. Combining the drought forecasting with the seasonal inflow forecasting may produce reasonable estimates of drought inflow from the probabilistic forecasting of seasonal inflow to a reservoir.

With the deepening of the diversification and openness of financial system, financial vulnerability, as an endogenous attribute of financial system, becomes an important measurement of financial security. Based on network analysis, we introduce network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with previous network curvature analysis method, CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

Changes in crude oil price affect the shipping freight market in three different channels. This study explores the dependence structure between oil prices and maritime freight rates to identify the strongest channel. Therefore, it investigates the relationship between oil prices and three major maritime freight rates; the Baltic Dry Index (BDI), the Baltic Dirty Tanker Index (BDTI), and the Baltic Clean Tanker Index (BCTI). We employ the decomposition method, not studied in the existing literature. The copula approach identifies the time-varying effects and asymmetry in the tail dependence structure between oil prices and freight rates. The main results of this analysis are as follows. The decomposed components display different conditional dependence patterns, and asymmetry is revealed in the upper and lower tail dependence. In the long run, we find more dependence in extreme periods like the financial crises. In short-run fluctuations, we find the dependence increases in an economic boom. The implications of the results suggest that dependence can vary over time and may change depending on extreme events, implying that the complementary strategies of the long run and short run should be different.

Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at extremely large and small thresholds is explored with particular emphasis on the skew-normal copula. Our numerical studies reveal that, when the correlation or skewness parameters are around at the boundary values, some asymptotic tail approximations of the skew-normal copulas proposed in the literature are not suitable to compute the measure of tail asymmetry with practically extremal thresholds.

In this study, a dynamic mixture copula is used to estimate the marginal expected shortfall in the South African insurance sector. While other studies assumed nonlinear dependence to be static over time, our model capture time-varying nonlinear dependence between institutions and the market. In order to capture time-varying nonlinear dependence, the generalized autoregressive score (GAS) is used to model the dynamic copula parameters. Furthermore, our study implements a ranking that expresses to what degree individual insurers are systemically important in South Africa. We use daily stock return of five South African insurers listed in the Johannesburg Stock Exchange (JSE) from November 13, 2007 to June 15, 2020. We find that Sanlam and Discovery contribute the most to systemic risk, while Santam is found to be the least contributor to the overall systemic risk in the South African insurance sector. Our findings would be of paramount importance for the South African regulators as they would be informed that not only banks are systemically important, but some insurers also are systemically important financial institutions. Hence, stricter regulation of these institutions in the form of higher capital and loss absorbency requirements could be required based on the individual business activities undertaken by the company.

Inflation and exchange rates have great influence on consumer prices especially on imports and exports. Exchange rate fluctuations create inefficiency and distort world prices whereas changes in inflation rates have a direct impact on consumer goods prices which incidentally include exchange rates. There is a direct interdependence between inflation and exchange rates and this paper is aimed at investigating this relationship in dynamic context. It tries to find out how changes in inflation and exchange rates impact on another by adopting the econometric and copula approaches. Both inflation and exchange rates data are susceptible to volatility clustering, possess fat tails and are skewed coupled with conditional heteroskedasticity. Hence we model the univariate distributions by using ARMA$(p,q)$-GARCH$(x,y)$ so as to capture the most important stylized features of inflation and exchange rates. A bivariate model is then constructed by coupling the marginal distributions of inflation and exchange rates using the survival Clayton copula. Empirical results from monthly inflation and exchange rates data show positive correlation between the two based on Kendall $\tau$ test which confirms that a change in inflation results in change of exchange rates an vice versa hence there is co-movement. Furthermore, by the Granger causality test, exchange rates spikes cause changes in inflation rates. The results of the study have implications on economic policy design and hedging strategies for traders on imports and exports.

This paper examines the dynamic dependence structure of crude oil and East Asian stock markets at multiple frequencies using wavelet and copulas. We also investigate risk management implications and diversification benefits of oil-stock portfolios by calculating and comparing risk and tail risk hedging performance. Our results provide strong evidence of time-varying dependence and asymmetric tail dependence between crude oil and East Asian stock markets at different frequencies. The level and fluctuation of their dependencies increase as time scale increases. Furthermore, we find the time-varying hedging benefits differ at investment horizons and reduced over the long run.

To improve the accuracy of short-term multi-energy load prediction models for integrated energy systems, the historical development law of the multi-energy loads must be considered. Moreover, understanding the complex coupling correlation of the different loads in the multi-energy systems and accounting for other load-influencing factors, such as weather, may further improve the forecasting performance of such models. In this study, a two-stage fuzzy optimization method is proposed for the feature selection and identification of the multi-energy loads. To enrich the information content of the prediction input feature, we introduced a copula correlation feature analysis in the proposed framework, which extracts the complex dynamic coupling correlation of multi-energy loads and applies Akaike information criterion (AIC) to evaluate the adaptability of the different copula models presented. Furthermore, we combined a NARX neural network with Bayesian optimization and an extreme learning machine model optimized using a genetic algorithm to effectively improve the feature fusion performances of the proposed multi-energy load prediction model. The effectiveness of the proposed short-term prediction model was confirmed by the experimental results obtained using the multi-energy load time-series data of an actual integrated energy system.

This paper investigates the dynamic tail dependence risk between BRICS economies and world energy market in the context of the COVID-19 financial crisis of 2020, to determine optimal investment decisions based on risk metrics. For this purpose, the study employs a combination of novel statistical techniques ranging from Markov Switching, GARCH and Vine copula. Using a dataset consisting of daily stock and world crude oil prices; we find high probability of transition between lower and higher volatility regimes. Furthermore, our results based on the C-Vine copula confirm the existence of two types of tail dependence: - symmetric tail dependence between South Africa and China; South Africa and Russia; and lower tail dependence between South Africa and India; South Africa and Brazil; South Africa and Oil. For the purpose of diversification in these markets, we formulate an asset allocation problem using C-vine copula-based returns and optimize it using Particle Swarm algorithm with a rebalancing strategy. The results show an inverse relationship between the risk contribution and asset allocation of South Africa and oil market supporting the existence of lower tail dependence between them. This suggests that when South African stocks are in distress, investors tend to shift their holdings in oil market. Similar results are found between China and oil. In the upper tail, South African asset allocation is found to have an inverse relationship with that of Brazil, Russia and India suggesting that these three markets might be good investment destinations when things are not good in South Africa and vice-versa.

Copulas are useful tools for modeling the dependence structure between two or more variables. Copulas are becoming a quite flexible tool in modeling dependence among the components of a multivariate vector, in particular to predict losses in insurance and finance. In this article, we study the dependence structure of some well-known real life insurance data (with two components mainly) and subsequently identify the best bivariate copula to model such a scenario via VineCopula package in R. Associated structural properties of these bivariate copulas are also discussed.

Investments in wind and solar power are driven by the aim to maximize the utilization of renewable energy (RE). This results in an increased concentration of wind farms at locations with higher average wind speeds and of solar panel installations at sites with higher average solar insolation. This is unfavourable for energy suppliers and for the overall economy when large power output fluctuations occur. Thus, when evaluating investment options for spatially distributed RE systems, it is necessary to model resource fluctuations and power output correlations between locations. In this paper, we propose a methodology for analyzing the spatial dependence, accurate modeling, and forecasting of wind power systems with special consideration to spatial dispersion of installation sites. We combine vine-copulas with the Kumaraswamy distribution to improve accuracy in forecasting wind power from spatially dispersed wind turbines and to model solar power generated at each location. We then integrate these methods to formulate an optimization model for allocating wind turbines and solar panels spatially, with an end goal of maximizing overall power generation while minimizing the variability in power output. A case study of wind and solar power systems in Central Ontario, Canada is also presented.

More and more works are using machine learning techniques while adopting supervisory control and data acquisition (SCADA) system for wind turbine anomaly or failure detection. While parameter selection is important for modelling a wind turbine’s health condition, only a few papers have been published focusing on this issue and in those papers interconnections among sub-components in a wind turbine are used to address this problem. However, merely the interconnections for decision making sometimes is too general to provide a parameter list considering the differences of each SCADA dataset. In this paper, a method is proposed to provide more detailed suggestions on parameter selection based on mutual information. Moreover, after proving that Copula, a multivariate probability distribution for which the marginal probability distribution of each variable is uniform is capable of simplifying the estimation of mutual information, an empirical copula based mutual information estimation method (ECMI) is introduced for an application. After that, a real SCADA dataset is adopted to test the method, and the results show the effectiveness of the ECMI in providing parameter selection suggestions when physical knowledge is not accurate enough.

According to the World Meteorological Organization, since 2000, there has been an increase in global flood-related disasters by 134 percent as compared to the two previous decades. Efficient flood risk management strategies necessitate a holistic approach to evaluating flood vulnerabilities and risks. Catastrophic losses can occur when the peak flow values in the rivers in a basin coincide. Therefore, estimating the joint flood risks in a region is vital, especially when frequent occurrences of extreme events are experienced. This study focuses on estimating the joint flood risks due to river flow extremes in the Grand River watershed in Canada. Determining the interdependence of floods at multiple locations using state-of-the-art tools, the associated damage probabilities, and their costs will be beneficial to various stakeholders, such as the insurance industry, the disaster management sector, and most importantly, the public.

This paper investigated reliability modeling for systems subject to dependent competing risks considering that the variation of failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of copula is symmetry. Then, A linear Wiener process model is applied to model performance degradation failure, and a multi-performance-degradation correlated-competition model based on a Copula function is constructed, which considers the correlated competition between multiperformance degradation failures. Lastly, the micromotor system is used to analyze the applicability of the proposed model for bivariate instances. demonstrating the rationality and effectiveness of the proposed model.

There is high confidence that climate change has increased the probability of concurrent temperature-precipitation extremes, changed their spatial-temporal variations, and affected the relationships between drivers of such natural hazards. However, the extent of such changes has been less investigated in Australia. Daily weather data (131 years, 1889-2019) at 700 grid cells (1◦ × 1◦) across Australia was obtained to calculate annual and seasonal mean daily maximum temperature (MMT) and total precipitation (TPR). A nonparametric multivariate copula framework was adopted to estimate the return period of compound hot-dry (CHD) events based on an ‘And’ hazard scenario (hotter than a threshold ‘And’ drier than a threshold). CHD extremes were defined as years with joint return periods of larger than 25 years. Mann-Kendall nonparametric tests was used to analyse trends in MMT and TPR as well as in the frequency of univariate and CHD extremes. A general cooling-wetting trend was observed over 1889-1989. Significant increasing trends were detected over 1990-2019 in the frequency and severity of hot extremes across the country while trends in dry extremes were mostly insignificant (and decreasing). Results showed a significant increase in the association between temperature and precipitation at various temporal scales. The frequency of CHD extremes was mostly stable over 1889-1989, but significantly increased between 1990 and 2019 at 44% of studied grid cells, mostly located in the north, south-east and south-west. Spatial homogeneity (i.e. connectedness) and propagation of extreme events from one grid cell to its neighbouring cells was investigated across Australia. It can be concluded that this connectedness has not significantly changed since 1889.

Target 9.c of the 2015 United Nations (UN) sustainable development goals (SDGs) specifically addresses increasing access to information and communication technology (ICT) resources, and striving for universal access to the internet by 2020. The present study seeks to evaluate the effectiveness of the youth related national strategies implemented in this regard by a select number of countries in the Middle East region. The study does so, by relying on a spatial bivariate copula regression analysis of data on youth respondents from five countries, extracted from the 2018 Program for international students’ assessment (PISA). Focusing specifically on evaluating the availability of ICT resources to the youth population, and also identifying the impact of ICT resources on youth subjective well-being in the region, we find that except for the UAE and Qatar that have above OECD average youth performance on the ICT resource index, youth from the remaining countries reported below OECD level average access to ICT resources. The within region cross-country comparative analysis of ICT resources availability to the youth population at home, also highlighted significant heterogeneity across the five countries, post 2015 SDG adoption by UN country members. Furthermore, looking at the impact of ICT resources on youth well-being, controlling for not only cross-country spatial correlations, and factors such as home educational resources, cultural possessions at home, parental occupation status, youth expected occupation status, economic and socio-cultural status, age, gender, and grade level in school; we found that every standard deviation increase in ICT resources to the youth population in the region raises their self-expressed sense of belonging in school by 1.88% standard deviations. Given the empowering nature of ICT resources to youth, and the potential of both to support national as well as regional economic development initiatives, a concerted effort to ease ICT resources diffusion by member countries in the middle east region could assist not only each country in its own development path, but also the region as a whole to live up to its growth potential by the 2030.

Traditional flood hazard analyses often rely on univariate probability distributions; however, in many coastal catchments, flooding is the result of complex hydrodynamic interactions between multiple drivers. For example, synoptic meteorological conditions can produce considerable rainfall-runoff, while also generating wind-driven elevated sea levels. When these drivers interact in space and time, they can exacerbate flood impacts; this phenomenon is known as compound flooding. In this paper, we build a Bayesian Network based on Gaussian copulas to generate the equivalent of 500 years of daily stochastic boundary conditions for a coastal watershed in Southeast Texas. In doing so, we overcome many of the limitations of conventional univariate approaches and are able to probabilistically represent compound floods caused by riverine and coastal interactions. We calculate the resulting water levels using a 1D steady-state hydraulic model and find that flood stages in the catchment are strongly affected by backwater effects from tributary inflows and downstream water levels. By comparing with a bathtub modeling approach, we show that simplifying the multivariate dependence between flood drivers can lead to an underestimation of flood impacts, highlighting that accounting for multivariate dependence is critical for the accurate representation of flood risk in coastal catchments prone to compound events.

A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of (Farlie-Gumbel-Morgenstern) FGM bivariate copula for constructing several dierent bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman's correlation coefficient rho,  and Kendall's tau . For illustrative purposes, one representative data set is utilized to exhibit the applicability of these proposed bivariate copula models.

This paper studies the contemporaneous relationship between S&P 500 index returns and log-increments of the market volatility index (VIX) via a nonparametric copula method. Specifically, we propose a conditional dependence index to investigate how the dependence between the two series varies across different segments of the market return distribution. We find that: (a) the two series exhibit strong, negative, extreme tail dependence; (b) the negative dependence is stronger in extreme bearish markets than in extreme bullish markets; (c) the dependence gradually weakens as the market return moves toward the center of its distribution, or in quiet markets. The unique dependence structure supports the VIX as a barometer of markets' mood in general. Moreover, applying the proposed method to the S&P 500 returns and the implied variance (VIX²), we find that the nonparametric leverage effect is much stronger than the nonparametric volatility feedback effect, although, in general, both effects are weaker than the dependence relation between the market returns and the log-increments of the VIX.

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events' statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3-D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west Coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-hr rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon's dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.

Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge either successively or in close succession. The trivariate distribution can demonstrate the risk of the compound phenomenon more realistically rather than considering each contributing factor independently or in a pairwise dependency. Recently vine copula has been recognized as the highly flexible approach to constructing a higher dimensional joint density framework. In such construction, parametric class copula with parametric univariate marginal distributions is often involved. Such incorporation can lack flexibility due to parametric functions with prior distribution assumptions about their univariate marginal and/or copula joint density. This study introduces the vine copula approach in a nonparametric setting by introducing Bernstein and Beta kernel copula density in establishing trivariate flood dependence. The proposed model is applied to 46 years of flood characteristics collected on the west coast of Canada. The univariate flood marginal distribution is modelled using nonparametric kernel density estimation (KDE). The 2-D Bernstein estimator and Beta kernel copulas estimator are tested independently in capturing pairwise dependencies to establish D-vine structure in a stage-wise nesting approach in three alternative ways, each by permutating the location of the conditioning variable. The best-fitted vine structure is selected using goodness-of-fit (GOF) test statistics. The performance of the nonparametric vine approach is also compared with the vine constructed in the parametric and semiparametric fitting procedure. Investigation reveals that the D-vine constructed using Bernstein copula with normal KDE marginals nonparametrically performed well in capturing dependence of the compound events. Finally, the derived nonparametric model is used in the estimation of trivariate OR- and AND-joint return periods, further employed in estimating failure probability (FP) statistics. The trivariate return periods for the AND-joint case are higher than for the OR-joint case for the same flood combination. Also, the trivariate flood hazard results in a high-value FP than bivariate and univariate events. Ignoring the trivariate dependence could result in the underestimation of FP

The Mann-Whitney effect is a measure for comparing survival distributions between two groups. The Mann-Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann-Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent each other, the traditional expression of the Mann-Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann-Witney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands (https://nkosuke.shinyapps.io/shiny_survival/). Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.