Probabilistic assessment of wind power plant energy potential through a copula-deep learning approach in decision trees

In the face of environmental degradation and diminished energy resources, there is an urgent need for clean, affordable, and sustainable energy solutions, which highlights the importance of wind energy. In the global transition to renewable energy sources, wind power has emerged as a key player that is in line with the Paris Agreement, the Net Zero Target by 2050, and the UN 2030 Goals, especially SDG-7. It is critical to consider the variable and intermittent nature of wind to efficiently harness wind energy and evaluate its potential. Nonetheless, since wind energy is inherently variable and intermittent, a comprehensive assessment of a prospective site's wind power generation potential is required. This analysis is crucial for stakeholders and policymakers to make well-informed decisions because it helps them assess financial risks and choose the best locations for wind power plant installations. In this study, we introduce a framework based on Copula-Deep Learning within the context of decision trees. The main objective is to enhance the assessment of the wind power potential of a site by exploiting the intricate and non-linear dependencies among meteorological variables through the fusion of copulas and deep learning techniques. An empirical study was carried out using wind power plant data from Turkey. This dataset includes hourly power output measurements as well as comprehensive meteorological data for 2021. The results show that acknowledging and addressing the non-independence of variables through innovative frameworks like the Copula-LSTM based decision tree approach can significantly improve the accuracy and reliability of wind power plant potential assessment and analysis in other real-world data scenarios. The implications of this research extend beyond wind energy to inform decision-making processes critical for a sustainable energy future.

A detailed study on quantification and modeling of drought characteristics using different copula families

This study delves into analyzing drought patterns in Baluchistan by applying copula-based bivariate probabilistic models complemented by Severity Duration Frequency (SDF) curves. The calculation of the Standardized Precipitation Index (SPI) hinges on monthly aggregate precipitation data from ten distinct sites compiled over six-month periods. After evaluating various parametric distributions, the Log-Normal distribution emerges as suitable for modeling drought severity and duration. A range of bivariate copulas is employed to simulate the characteristics of drought severity and duration, which are then compared against observed data. Remarkably, the Gumbel copula classified as an extreme value copula-outperforms its counterparts according to diverse statistical benchmarks. By utilizing the dependence function, we derive the conditional distribution of drought variables: severity and duration. These conditional distributions subsequently inform the calculation of return periods, forming the basis for constructing SDF diagrams at fixed recurrence levels across the study region. The study's finding indicates that a severe drought could occur over the region with higher return periods for a specific duration. The implications of this research are significant, showcasing the potential of copula-based joint modeling techniques to generate frequency curves for drought severity and duration. This development holds promise for effective water resource management and the formulation of strategies to mitigate the impact of drought in vulnerable regions.

Statistical actuarial estimation of the Capitation Payment Unit from copula functions and deep learning: historical comparability analysis for the Colombian health system, 2015-2021

The Capitation Payment Unit (CPU) financing mechanism constitutes more than 70% of health spending in Colombia, with a budget allocation of close to 60 trillion Colombian pesos for the year 2022 (approximately 15.7 billion US dollars). This article estimates actuarially, using modern techniques, the CPU for the contributory regime of the General System of Social Security in Health in Colombia, and compares it with what is estimated by the Ministry of Health and Social Protection. Using freely available information systems, by means of statistical copulas functions and artificial neural networks, pure risk premiums are calculated between 2015 and 2021. The study concludes that the weights by risk category are systematically different, showing historical pure premiums surpluses in the group of 0-1 years and deficits (for the regions normal and cities) in the groups over 54 years of age.

Quantitative risk assessment of typhoon storm surge for multi-risk sources

Typhoon storm surge (TSS) is a complex marine disaster affected by multi-risk sources. Quantitative risk assessment is an important prerequisite for identifying risk areas and designing risk reduction strategies. This paper aims to propose a rapid, accurate, and comprehensive quantitative risk assessment method for TSS under multi-risk sources, including disaster occurrence probability and severity. First, identify the primary risk sources according to the disaster-causing mechanism of TSS. Then, based on the official public data from 1989 to 2020, the dependence structure among multi-risk sources is constructed using Copulas to calculate the probability of each superposition scenario. Meanwhile, build visual scenario databases employing Geographical Information System (GIS) techniques. Subsequently, the extent and depth of inundation are translated into economic risk and population risk using GIS and depth-damage functions. Finally, taking the "Mangkhut" as a case study, the method's feasibility and accuracy are verified. The results show that the primary risk sources of TSS are storm tide, astronomical tide and coastal waves. The Gumbel Copula is optimal, with OLS (ordinary least squares) and D of 0.0186 and 0.1831, respectively. The probability assessment under different superposition scenarios indicates that the greatest threat of TSS in Guangzhou comes from the storm tide and the astronomical tide. As for the "Mangkhut" case study in Jiangmen City, the assesses occurrence probability is 0.0355%, the accuracy of economic risk assessment (except mariculture) is 95.28%, and the accuracy of population risk assessment is 98.60%. Residences and the disaster-bearing bodies in 0-3 m inundation depth are most severely affected by TSS disasters. Measures such as locating residential and important buildings away from the shoreline (at least 10 km) and ground (above 3 m), formulating disaster emergency plans, and developing the forecast and prevention of storm tides and astronomical tides will help ensure the safety of residents' life and property. This paper provides an efficient and accurate method, which is of great significance for disaster control, sustainable development, and decision-making.

Tail-risk spillovers from China to G7 stock market returns during the COVID-19 outbreak: A market and sectoral analysis

This study uses a combination of copulas and CoVaR to investigate risk spillovers from China to G7 countries before and during the COVID-19 pandemic. Using daily data on stock and equity sectors for the period from January 1, 2013 to June 9, 2021, the main empirical results show that, before the COVID-19 pandemic, stock markets were positively related and systemic risk was comparable for all countries. However, during the COVID-19 outbreak, the level of dependence increased for all G7 countries and the upside-downside risk spillovers become on average higher for all stock markets, with the exception of Japan. Our results also provide evidence of higher market risk exposure to information from China for the technology and energy sectors. Moreover, we find an asymmetric risk spillover from China to the G7 stock markets, with higher intensity in downside risk spillovers before and during COVID-19 spread.

Comparison of Value at Risk (VaR) Multivariate Forecast Models

We investigate the performance of VaR (Value at Risk) forecasts, considering different multivariate models: HS (Historical Simulation), DCC-GARCH (Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity) with normal and Student's t distribution, GO-GARCH (Generalized Orthogonal-Generalized Autoregressive Conditional Heteroskedasticity), and copulas Vine (C-Vine, D-Vine, and R-Vine). For copula models, we consider that marginal distribution follow normal, Student's t and skewed Student's t distribution. We assessed the performance of the models using stocks belonging to the Ibovespa index during the period from January 2012 to April 2022. We build portfolios with 6 and 12 stocks considering two strategies to form the portfolio weights. We use a rolling estimation window of 500 and 1000 observations and 1%, 2.5%, and 5% as significance levels for the risk estimation. To evaluate the quality of the risk forecasts, we compute the realized loss and cost. Our results show that the performance of the models is sensitive to the use of different significance levels, rolling windows, and strategies to determine portfolio weights. Furthermore, we find that the model that presents the best trade-off between the costs from risk overestimation and underestimation does not coincide with the model suggested by the realized loss.

A static and dynamic copula-based ARIMA-fGARCH approach to determinants of carbon dioxide emissions in Argentina

This paper attempts to model both static and dynamic dependence structures and measure impacts of energy consumptions (both renewable (EC) and non-renewable (REN) energies), economic globalization (GLO), and economic growth (GDP) on carbon dioxide (CO₂) emissions in Argentina over the period 1970-2020. For analyses purpose, the current research deploys the novel static and dynamic copula-based ARIMA-fGARCH with different submodels. The static bivariate copula results show that the growth rates of the pairs EC-CO₂ and GDP-CO₂ are asymmetrically positive co-movements and have high left tail (extreme) dependencies, implying that the increase in non-renewable energy and economic growth can critically contribute to the environmental degradation, and the decrease in the consumption of non-renewable energy at a high level will consequently reduce the CO₂ emissions at the same level. Based on several copula-based dependence measures, we document that between the two factors, the non-renewable energy has a stronger impact than the economic growth regarding the CO₂ emissions. On the other hand, the growth rates of both economic globalization and renewable energy symmetrically negatively co-move with the growth rates of the CO₂ emissions, but they have no extreme dependencies, indicating that these factors contribute to Argentina's environmental quality, in which the factor of renewable energy has a greater impact. Furthermore, the dynamic copula outcomes show that the (tail) dependencies of CO₂ emissions on the non-renewable energy and economic growth are time-varying, while the pairs REN-CO₂ and GLO-CO₂ possess only dynamic dependencies, but no dynamic tail dependencies. Moreover, through the dynamic copula-based dependence, the environmental Kuznets curve (EKC) hypothesis can be estimated and illustrated explicitly. In addition, we leverage multivariate vine copulas for modelling dependence structures of the five variables simultaneously, which can reveal rich information regarding conditional associations among the relevant variables. Some policy implications are also provided to mitigate CO₂ emissions.

A locally relevant framework for assessing the risk of sea level rise under changing temperature conditions: Application in New Caledonia, Pacific Ocean

Sea level rise is a key feature in a warmer world and its impact can be seen globally. Assessing climate change-induced sea level rise, therefore, is urgently needed particularly in small island nations, where the threats of sea level rise are immediate, but the level of preparedness is low. Here, we propose a stochastic simulator to link changes in Mean Annual Temperature (MAT) to Mean Annual Sea Level (MASEL) at the local scale. This is through what-if scenarios that are developed based on the association between local temperature and sea level. The model can provide a basis for a bottom-up impact assessment by addressing limitations of applying large-scale projections in small islands and facilitating the accessibility of the impact assessment to stakeholders. For this purpose, we decompose the MAT and MASEL signals into their linear trend and autocorrelation components as well as independent and identically distributed residual terms. We further explore the association between trend and residual terms of MAT and MASEL. If such dependencies exist, scenarios of sea level can be synthesized based on the trend and residual terms of temperature. We use linear regression to link trends of MAT and MASEL, and copulas to formulate dependencies between residuals. This allows stochastic sampling of MASEL conditioned to trend and random variability in MAT. This framework is used for retrospective and prospective simulations of MASEL in Nouméa, the capital city of New Caledonia, the Pacific. We set up six different model configurations for developing the stochastic sampler, each including various parametric options. By selecting the best setup from each configuration, we provide a multi-model stochastic projection of MASEL, assuming the persistence in current long-term trend in MAT and MASEL. We demonstrate how such simulations can be used for a risk-based impact assessments and discuss sources of uncertainty in future projections.

The nexus between black and digital gold: evidence from US markets

In the context of the debate on cryptocurrencies as the 'digital gold', this study explores the nexus between the Bitcoin and US oil returns by employing a rich set of parametric and non-parametric approaches. We examine the dependence structure of the US oil market and Bitcoin through Clayton copulas, normal copulas, and Gumbel copulas. Copulas help us to test the volatility of these dependence structures through left-tailed, right-tailed or normal distributions. We collected daily data from 5 February 2014 to 24 January 2019 on Bitcoin prices and oil prices. The data on bitcoin prices were extracted from coinmarketcap.com. The US oil prices were collected from the Federal Reserve Economic Data source. Maximum pseudo-likelihood estimation was applied to the dataset and showed that the US oil returns and Bitcoin are highly vulnerable to tail risks. The multiplier bootstrap-based goodness-of-fit test as well as Kendal plots also suggest left-tail dependence, and this adds to the robustness of the results. The stationary bootstrap test for the partial cross-quantilogram indicates which quantile in the left tail has a statistically significant relationship between Bitcoin and US oil returns. The study has crucial implications in terms of portfolio diversification using cryptocurrencies and oil-based hedging instruments.

Asymmetric dependence of intraday frequency components in the Brazilian stock market

The multivariate dependence plays an important role in financial instrument management. Due to the inherent characteristics in the financial market, such as heavy tails in the returns unconditional distribution and asymmetry between gain and loss, we obtained the asymmetric dependence structure in different short-term variation scales based on the wavelet technique MODWT. The study sought to capture the relations between financial returns represented by its frequency components. Intraday returns series was used in the 15-min sampling interval from stocks and applied the D-Vine pair-copula to decompose in trade frequencies of 15 min, 1 h, 1 day, and 1 week with margin adjustments of ARIMA-APARCH class and BB7 copula function, responsible for measuring the dependence on tails. The results indicated the prevalence of a high dependence during market upturns, rising over the analyzed frequencies. Being an important tool in financial management and allowing short-term strategies of diversification.

Monthly drought prediction based on ensemble models

Drought is a natural hazard, which is a result of a prolonged shortage of precipitation, high temperature and change in the weather pattern. Drought harms society, the economy and the natural environment, but it is difficult to identify and characterize. Many areas of Pakistan have suffered severe droughts during the last three decades due to changes in the weather pattern. A drought analysis with the incorporation of climate information has not yet been undertaken in this study region. Here, we propose an ensemble approach for monthly drought prediction and to define and examine wet/dry events. Initially, the drought events were identified by the short term Standardized Precipitation Index (SPI-3). Drought is predicted based on three ensemble models i.e., Equal Ensemble Drought Prediction (EEDP), Weighted Ensemble Drought Prediction (WEDP) and the Conditional Ensemble Drought Prediction (CEDP) model. Besides, two weighting procedures are used for distributing weights in the WEDP model, such as Traditional Weighting (TW) and the Weighted Bootstrap Resampling (WBR) procedure. Four copula families (i.e., Frank, Clayton, Gumbel and Joe) are used to explain the dependency relation between climate indices and precipitation in the CEDP model. Among all four copula families, the Joe copula has been found suitable for most of the times. The CEDP model provides better results in terms of accuracy and uncertainty as compared to other ensemble models for all meteorological stations. The performance of the CEDP model indicates that the climate indices are correlated with a weather pattern of four meteorological stations. Moreover, the percentage occurrence of extreme drought events that have appeared in the Multan, Bahawalpur, Barkhan and Khanpur are 1.44%, 0.57%, 2.59% and 1.71%, respectively, whereas the percentage occurrence of extremely wet events are 2.3%, 1.72%, 0.86% and 2.86%, respectively. The understanding of drought pattern by including climate information can contribute to the knowledge of future agriculture and water resource management.

A study of dependency features of spike trains through copulas

Despite the progresses of statistical and machine learning techniques, simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered. Discerning the presence of direct links between neurons from data is still a not completely solved problem. We propose the use of copulas, to enlarge the number of tools for detecting the network structure, pursuing on a research direction we started in Sacerdote et al. (2012). Here, our aim is to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and indirect interactions.

Diversity and motif conservation in protein 3D structural landscape: exploration by a new multivariate simulation method

In this paper, diversity and conservation in the 'landscape' of random variation of protein tertiary structures are explored for quantitative feature-vector models of major types of functionally important 3D structural motifs. For this, I have deployed a recently developed nonparametric regression (NPR)-based multidimensional copula method of simulation. Apart from improved accuracy of multidimensional random sample generation, the simulation provides additional insight into diversity in the protein structural landscape in terms of random variation in the feature-vector. It shows the relative importance of several features, with biological implications, in conservation of motifs. Mapping of this landscape in distance-preserving 2D eigenspace also shows consistency in demarcation of different motif classes and preservation of their characteristic patterns in this 2D space.

Rank correlation under categorical confounding

Rank correlation is invariant to bijective marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation for continuous variables developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

Modeling Correlated Discrete Uncertainties in Event Trees with Copulas

Modeling the dependence between uncertainties in decision and risk analyses is an important part of the problem structuring process. We focus on situations where correlated uncertainties are discrete, and extend the concept of the copula-based approach for modeling correlated continuous uncertainties to the representation of correlated discrete uncertainties. This approach reduces the required number of probability assessments significantly compared to approaches requiring direct estimates of conditional probabilities. It also allows the use of multiple dependence measures, including product moment correlation, rank order correlation and tail dependence, and parametric families of copulas such as normal copulas, t-copulas, and Archimedean copulas. This approach can be extended to model the dependence between discrete and continuous uncertainties in the same event tree.

A unifying framework for marginalized random intercept models of correlated binary outcomes

We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized random intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.