Wind Energy: Forecasting Challenges for its Operational Management

Renewable energy sources, especially wind energy, are to play a larger role in providing electricity to industrial and domestic consumers. This is already the case today for a number of European countries, closely followed by the US and high growth countries, for example, Brazil, India and China. There exist a number of technological, environmental and political challenges linked to supplementing existing electricity generation capacities with wind energy. Here, mathematicians and statisticians could make a substantial contribution at the interface of meteorology and decision-making, in connection with the generation of forecasts tailored to the various operational decision problems involved. Indeed, while wind energy may be seen as an environmentally friendly source of energy, full benefits from its usage can only be obtained if one is able to accommodate its variability and limited predictability. Based on a short presentation of its physical basics, the importance of considering wind power generation as a stochastic process is motivated. After describing representative operational decision-making problems for both market participants and system operators, it is underlined that forecasts should be issued in a probabilistic framework. Even though, eventually, the forecaster may only communicate single-valued predictions. The existing approaches to wind power forecasting are subsequently described, with focus on single-valued predictions, predictive marginal densities and space-time trajectories. Upcoming challenges related to generating improved and new types of forecasts, as well as their verification and value to forecast users, are finally discussed.Comment: Published in at http://dx.doi.org/10.1214/13-STS445 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Copula-based statistical modelling of synoptic-scale climate indices for quantifying and managing agricultural risks in australia

Australia is an agricultural nation characterised by one of the most naturally diverse climates in the world, which translates into significant sources of risk for agricultural production and subsequent farm revenues. Extreme climatic events have been significantly affecting large parts of Australia in recent decades, contributing to an increase in the vulnerability of crops, and leading to subsequent higher risk to a large number of agricultural producers. However, attempts at better managing climate related risks in the agricultural sector have confronted many challenges. First, crop insurance products, including classical claim-based and index-based insurance, are among the financial implements that allow exposed individuals to pool resources to spread their risk. The classical claim-based insurance indemnifies according to a claim of crop loss from the insured customer, and so can easily manage idiosyncratic risk, which is the case where the loss occurs independently.Nevertheless, the existence of systemic weather risk (covariate risk), which is the spread of extreme events over locations and times (e.g., droughts and floods), has been identified as the main reason for the failure of private insurance markets, such as the classical multi-peril crop insurance, for agricultural crops. The index-based insurance is appropriate to handle systemic but not idiosyncratic risk. The indemnity payments of the index-based insurance are triggered by a predefined threshold of an index (e.g., rainfall), which is related to such losses. Since the covariate nature of a climatic event, it sanctions the insurers to predict losses and ascertain indemnifications for a huge number of insured customers across a wide geographical area. However, basis risk, which is related to the strength of the relationship between the predefined indices used to estimate the average loss by the insured community and the actual loss of insured assets by an individual, is a major barrier that hinders uptake of the index-based insurance. Clearly, the high basis risk, which is a weak relationship between the index and loss, destroys the willingness of potential customers to purchase this insurance product. Second, the impact of multiple synoptic-scale climate mode indices (e.g., Southern Oscillation Index (SOI) and Indian Ocean Index (IOD)) on precipitation and crop yield is not identical in different spatial locations and at different times or seasons across the Australian continent since the influence of large-scale climate heterogeneous over the different regions. The occurrence, role, and amplitude of synoptic-scale climate modes contributing to the variability of seasonal crop production have shifted in recent decades. These variables generally complicate the climate and crop yield relationship that cannot be captured by traditional modelling and analysis approaches commonly found in published agronomic literature such as linear regression. In addition, the traditional linear analysis is not able to model the nonlinear and asymmetric interdependence between extreme insurance losses, which may occur in the case of systemic risk. Relying on the linear method may lead to the problem that different behaviour may be observed from joint distributions, particularly in the upper and lower regions, with the same correlation coefficient. As a result, the likelihood of extreme insurance losses can be underestimated or overestimated that lead to inaccuracies in the pricing of insurance policies. Another alternative is the use of the multivariate normal distribution, where the joint distribution is uniquely defined using the marginal distributions of variables and their correlation matrix. However, phenomena are not always normally distributed in practice. It is therefore important to develop new, scientifically verified, strategic measures to solve the challenges as mentioned above in order to support mitigating the influences of the climate-related risk in the agricultural sector. Copulas provide an advanced statistical approach to model the joint distribution of multivariate random variables. This technique allows estimating the marginal distributions of individual variables independently with their dependence structures. It is clear that the copula method is superior to the conventional linear regression since it does not require variables have to be normally distributed and their correlation can be either linear or non-linear. This doctoral thesis therefore adopts the advanced copula technique within a statistical modelling framework that aims to model: (1) The compound influence of synoptic-scale climate indices (i.e., SOI and IOD) and climate variables (i.e., precipitation) to develop a probabilistic precipitation forecasting system where the integrated role of different factors that govern precipitation dynamics are considered; (2) The compound influence of synoptic-scale climate indices on wheat yield; (3) The scholastic interdependencies of systemic weather risks where potential adaptation strategies are evaluated accordingly; and (4) The risk-reduction efficiencies of geographical diversifications in wheat farming portfolio optimisation. The study areas are Australia’s agro-ecological (i.e., wheat belt) zones where major seasonal wheat and other cereal crops are grown. The results from the first and second objectives can be used for not only forecasting purposes but also understanding the basis risk in the case of pricing climate index-based insurance products. The third and fourth objectives assess the interactions of drought events across different locations and in different seasons and feasible adaptation tools. The findings of these studies can provide useful information for decision-makers in the agricultural sector. The first study found the significant relationship between SOI, IOD, and precipitation. The results suggest that spring precipitation in Australia, except for the western part, can be probabilistically forecasted three months ahead. It is more interesting that the combination of SOI and IOD as the predictors will improve the performance of the forecast model. Similarly, the second study indicated that the largescale climate indices could provide knowledge of wheat crops up to six months in advance. However, it is noted that the influence of different climate indices varies over locations and times. Furthermore, the findings derived from the third study demonstrated the spatio-temporally stochastic dependence of the drought events. The results also prove that time diversification is potentially more effective in reducing the systemic weather risk compared to spatially diversifying strategy. Finally, the fourth objective revealed that wheat-farming portfolio could be effectively optimised through the geographical diversification. The outcomes of this study will lead to the new application of advanced statistical tools that provide a better understanding of the compound influence of synoptic-scale climatic conditions on seasonal precipitation, and therefore on wheat crops in key regions over the Australian continent. Furthermore, a comprehensive analysis of systemic weather risks performed through advanced copula-statistical models can help improve and develop novel agricultural adaptation strategies in not only the selected study region but also globally, where climate extreme events pose a serious threat to the sustainability and survival of the agricultural industry. Finally, the evaluation of the effectiveness of diversification strategies implemented in this study reveals new evidence on whether the risk pooling methods could potentially mitigate climate risks for the agricultural sector and subsequently, help farmers in prior preparation for uncertain climatic events

Development of a copula-based particle filter (CopPF) approach for hydrologic data assimilation under consideration of parameter interdependence

National Natural Science Foundation of China, the National Key Research and Development Plan, and the Natural Sciences and Engineering Research Council of Canad

Development of a maximum entropy-Archimedean copula-based bayesian network method for streamflow frequency analysis-A case study of the Kaidu River Basin, China

Frequency analysis of streamflow is critical for water-resources system planning, water conservancy projects and the mitigation of hydrological extremes events. In this study, a maximum entropy-Archimedean copula-based Bayesian network (MECBN) method has been proposed for frequency analysis of monthly streamflow in the Kaidu River Basin, which integrates the maximum entropy-Archimedean copula (MEAC) and Bayesian network methods into a general framework. MECBN is effective for representing the uncertainties that exist in model representation, preserving the distributional characteristics of streamflow records and addressing the correlation structure between streamflow pairs. Application to the Kaidu River Basin shows a good performance of MECBN in describing the historical data of this basin in China. The results indicate that the interactions between two adjacent monthly streamflow pairs are non-linear. There is upper tail dependence between monthly streamflow pairs. The dependence coefficients including Spearman’s rho, Kendall’s tau, and the upper tail dependence coefficient are in inverse proportion of monthly streamflow values in the Kaidu River Basin, due to the fact that other factors (i.e., rainfall, snow melting, evapotranspiration rate and requirement of water use) provide more contributions to the streamflow in the flooding season. These findings can be used for providing vital information in the prevention and control of hydrological extremes and to further water resources planning in Kaidu River Basin.Training Programme Foundation for the Beijing Municipal Excellent Talents, National Sciences Foundation and [National Natural Science Foundation of Chin

A Survey of Systemic Risk Analytics

We provide a survey of 31 quantitative measures of systemic risk in the economics and finance literature, chosen to span key themes and issues in systemic risk measurement and management. We motivate these measures from the supervisory, research, and data perspectives in the main text and present concise definitions of each risk measure—including required inputs, expected outputs, and data requirements—in an extensive Supplemental Appendix. To encourage experimentation and innovation among as broad an audience as possible, we have developed an open-source Matlab® library for most of the analytics surveyed, which, once tested, will be accessible through the Office of Financial Research (OFR) at http://www.treasury.gov/initiatives/wsr/ofr/Pages/default.aspx.United States. Dept. of the Treasury. Office of Financial ResearchMassachusetts Institute of Technology. Laboratory for Financial EngineeringNational Science Foundation (U.S.) (Grant ECCS-1027905

WIND POWER PROBABILISTIC PREDICTION AND UNCERTAINTY MODELING FOR OPERATION OF LARGE-SCALE POWER SYSTEMS

Over the last decade, large scale renewable energy generation has been integrated into power systems. Wind power generation is known as a widely-used and interesting kind of renewable energy generation around the world. However, the high uncertainty of wind power generation leads to some unavoidable error in wind power prediction process; consequently, it makes the optimal operation and control of power systems very challenging. Since wind power prediction error cannot be entirely removed, providing accurate models for wind power uncertainty can assist power system operators in mitigating its negative effects on decision making conditions. There are efficient ways to show the wind power uncertainty, (i) accurate wind power prediction error probability distribution modeling in the form of probability density functions and (ii) construction of reliable and sharp prediction intervals. Construction of accurate probability density functions and high-quality prediction intervals are difficult because wind power time series is non-stationary. In addition, incorporation of probability density functions and prediction intervals in power systems’ decision-making problems are challenging. In this thesis, the goal is to propose comprehensive frameworks for wind power uncertainty modeling in the form of both probability density functions and prediction intervals and incorporation of each model in power systems’ decision-making problems such as look-ahead economic dispatch. To accurately quantify the uncertainty of wind power generation, different approaches are studied, and a comprehensive framework is then proposed to construct the probability density functions using a mixture of beta kernels. The framework outperforms benchmarks because it can validly capture the actual features of wind power probability density function such as main mass, boundaries, high skewness, and fat tails from the wind power sample moments. Also, using the proposed framework, a generic convex model is proposed for chance-constrained look-ahead economic dispatch problems. It allows power system operators to use piecewise linearization techniques to convert the problem to a mixed-integer linear programming problem. Numerical simulations using IEEE 118-bus test system show that compared with widely used sequential linear programming approaches, the proposed mixed-integer linear programming model leads to less system’s total cost. A framework based on the concept of bandwidth selection for a new and flexible kernel density estimator is proposed for construction of prediction intervals. Unlike previous related works, the proposed framework uses neither a cost function-based optimization problem nor point prediction results; rather, a diffusion-based kernel density estimator is utilized to achieve high-quality prediction intervals for non-stationary wind power time series. The proposed prediction interval construction framework is also founded based on a parallel computing procedure to promote the computational efficiency for practical applications in power systems. Simulation results demonstrate the high performance of the proposed framework compared to well-known conventional benchmarks such as bootstrap extreme learning machine, lower upper bound estimation, quantile regression, auto-regressive integrated moving average, and linear programming-based quantile regression. Finally, a new adjustable robust optimization approach is used to incorporate the constructed prediction intervals with the proposed fuzzy and adaptive diffusion estimator-based prediction interval construction framework. However, to accurately model the correlation and dependence structure of wind farms, especially in high dimensional cases, C-Vine copula models are used for prediction interval construction. The simulation results show that uncertainty modeling using C-Vine copula can lead the system operators to get more realistic sense about the level of overall uncertainty in the system, and consequently more conservative results for energy and reserve scheduling are obtained

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research

Four essays on financial risk quantification

136 p.Esta tesis tiene como objetivo analizar el desempeño de medidas de riesgo como el Value-at-Risk (VaR) y (recientemente propuesta por el Comité de Basilea) de Expected Shortfall (ES), principalmente para cuantificar riesgo de mercado, con diferentes modelos distribucionales, como por ejemplo la distribución Gaussiana (como modelo base), y varias distribuciones que presentan colas pesadas como la distribución t de Student, distribución de Pareto generalizada (GPD, por sus siglas inglés), la distribución ¿-estable, distribución g-h, y la distribución Gram-Charlier. Para tal fin se emplean diferentes activos como índices bursátiles de energía tradicional y de activos financieros sostenibles. Dada la preocupación en los mercados financieros por el (ab)uso de activos como Exchange-traded funds (ETFs), en especial los ETFs apalancados (LETFs, por sus siglas en inglés), estos activos también son analizados en la presente tesis. Aunque Expected Shortfall es una medida coherente al riesgo, es conocido que esta medida no cumple con la propiedad de elicitabilidad, una propiedad deseable en pronósticos con fines de validación de modelos (backtesting). Esta tesis implementa dos recientes técnicas de validación de ES con buenos resultados e implicaciones en cuanto a estabilidad financiera. Finalmente se realiza una revisión de la reciente propuesta del Comité de Basilea para cuantificar riesgo operacional

Four essays on financial risk quantification

136 p.Esta tesis tiene como objetivo analizar el desempeño de medidas de riesgo como el Value-at-Risk (VaR) y (recientemente propuesta por el Comité de Basilea) de Expected Shortfall (ES), principalmente para cuantificar riesgo de mercado, con diferentes modelos distribucionales, como por ejemplo la distribución Gaussiana (como modelo base), y varias distribuciones que presentan colas pesadas como la distribución t de Student, distribución de Pareto generalizada (GPD, por sus siglas inglés), la distribución ¿-estable, distribución g-h, y la distribución Gram-Charlier. Para tal fin se emplean diferentes activos como índices bursátiles de energía tradicional y de activos financieros sostenibles. Dada la preocupación en los mercados financieros por el (ab)uso de activos como Exchange-traded funds (ETFs), en especial los ETFs apalancados (LETFs, por sus siglas en inglés), estos activos también son analizados en la presente tesis. Aunque Expected Shortfall es una medida coherente al riesgo, es conocido que esta medida no cumple con la propiedad de elicitabilidad, una propiedad deseable en pronósticos con fines de validación de modelos (backtesting). Esta tesis implementa dos recientes técnicas de validación de ES con buenos resultados e implicaciones en cuanto a estabilidad financiera. Finalmente se realiza una revisión de la reciente propuesta del Comité de Basilea para cuantificar riesgo operacional