Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range ...Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs.Two special cases of regular vine copulas,C-vine and D-vine copulas,have been extensively investigated in the literature.We propose the Python package,pyvine,for modeling,sampling and testing a more generalized regular vine copula(R-vine for short).R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way.The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization.R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions.Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data E and then tests the hypothesis H^(∗)_(0):E∼C_(⊥)by using Anderson–Darling statistic,where C_(⊥)is the independence copula.Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic.The computing of related functions of copulas such as cumulative distribution functions,Hfunctions and inverse H-functions often meets with the problem of overflow.We solve this problem by reinvestigating the following six families of bivariate copulas:Normal,Student t,Clayton,Gumbel,Frank and Joe’s copulas.Approximations of the above related functions of copulas are given when the overflow occurs in the computation.All these are implemented in a subpackage bvcopula,in which subroutines are written in Fortran and wrapped into Python and,hence,good performance is guaranteed.展开更多
Owing to the uncertainty and volatility of wind energy,forecasted wind power scenarios with proper spatio-temporal correlations are needed in various decision-making problems involving power systems.In this study,fore...Owing to the uncertainty and volatility of wind energy,forecasted wind power scenarios with proper spatio-temporal correlations are needed in various decision-making problems involving power systems.In this study,forecasted scenarios are generated from an estimated multi-variate distribution of multiple regional wind farms.According to the theory of copulas,marginal distributions and the dependence structure of multi-variate distribution are modeled through the proposed distance-weighted kernel density estimation method and the regular vine(R-vine)copula,respectively.Owing to the flexibility of decomposing correlations of high dimensions into different types of pair-copulas,the R-vine copula provides more accurate results in describing the complicated dependence of wind power.In the case of 26 wind farms located in East China,highquality forecasted scenarios as well as the corresponding probabilistic forecasting and point forecasting results are obtained using the proposed method,and the results are evaluated using a comprehensive verification framework.展开更多
碳排放交易市场的建立,是一个基于经济学理论来解决气候变暖问题的具有价值的途径,其目的是发展低碳经济。在欧盟排放交易体系一级市场上,以欧盟排放配额(European Union Allowances,EUA)作为主要交易标的物的碳排放权交易市场已经成为...碳排放交易市场的建立,是一个基于经济学理论来解决气候变暖问题的具有价值的途径,其目的是发展低碳经济。在欧盟排放交易体系一级市场上,以欧盟排放配额(European Union Allowances,EUA)作为主要交易标的物的碳排放权交易市场已经成为一个重要的新兴贸易市场。随着碳排放权交易市场的不断发展,该市场的资本化程度逐渐深化,其金融属性也日益显著,并逐步融入到国际资本市场体系之中。与其它资本市场相类似,碳排放权交易市场之间也存在着复杂的非线性相关关系,而Copula函数可以用来捕捉这种相依结构特征。因此,文章选取欧盟排放配额(EUA)期货的日价格时间序列数据,首先假设新息序列服从学生t分布,运用ARMA-GARCH模型对经调整的对数收益率序列进行过滤,采用极大似然方法估计模型的参数,并得到残差序列,同时将其标准化而得到标准化残差;然后,将Kendall’s tau秩相关系数作为权重,采用最大生成树算法(maximum spanning tree algorithm)的序贯Copula选择方法构建合适的规则藤Copula模型,并运用基于序贯的极大似然方法估计规则藤Copula模型,以描述碳排放权交易市场之间复杂的相依结构特征。研究结果发现:在无条件下,t-copula函数可以较好地捕捉碳排放权市场之间的相依关系,说明市场存在明显的对称尾部;在Dec10EUA、Dec12EUA、Dec13EUA市场相依结构固定下,Dec11EUA与Dec14EUA市场之间的相依结构可以采用Gaussian copula函数来描述,而在Dec10EUA、Dec13EUA市场相依结构确定不变情形下,Dec12EUA与Dec14EUA市场之间的相依结构则适合采用Frank copula函数来捕捉,说明这些市场之间并没有出现尾部特征。进一步地,文章分别选择White信息矩阵等式拟合优度检验和基于概率积分转换(probability integral transform,PIT)与经验Copula过程(empirical copula process,ECP)混合方法的拟合优度检验,并基于Bootstrap方法,以Cramer von Mises(Cv M)检验统计量作为度量测度,来对模型进行拟合优度的检验。研究发现,构建的规则藤Copula模型能够较好地捕捉碳排放权市场之间的相依结构。这一研究结果,为准确探讨碳排放权交易市场之间、碳排放权交易市场与其它资本市场之间套期保值策略提供了一定的参考意义,也有利于提高碳排放权市场产品定价的准确度。展开更多
Scenario forecasting methods have been widely studied in recent years to cope with the wind power uncertainty problem. The main difficulty of this problem is to accurately and comprehensively reflect the time-series c...Scenario forecasting methods have been widely studied in recent years to cope with the wind power uncertainty problem. The main difficulty of this problem is to accurately and comprehensively reflect the time-series characteristics and spatial-temporal correlation of wind power generation. In this paper, the marginal distribution model and the dependence structure are combined to describe these complex characteristics. On this basis, a scenario generation method for multiple wind farms is proposed. For the marginal distribution model, the autoregressive integrated moving average-generalized autoregressive conditional heteroskedasticity-t (ARIMA-GARCH-t) model is proposed to capture the time-series characteristics of wind power generation. For the dependence structure, a time-varying regular vine mixed Copula (TRVMC) model is established to capture the spatial-temporal correlation of multiple wind farms. Based on the data from 8 wind farms in Northwest China, sufficient scenarios are generated. The effectiveness of the scenarios is evaluated in 3 aspects. The results show that the generated scenarios have similar fluctuation characteristics, autocorrelation, and crosscorrelation with the actual wind power sequences.展开更多
基金This work was supported by the NNSF of China(Nos.11371340,71871208).
文摘Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs.Two special cases of regular vine copulas,C-vine and D-vine copulas,have been extensively investigated in the literature.We propose the Python package,pyvine,for modeling,sampling and testing a more generalized regular vine copula(R-vine for short).R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way.The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization.R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions.Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data E and then tests the hypothesis H^(∗)_(0):E∼C_(⊥)by using Anderson–Darling statistic,where C_(⊥)is the independence copula.Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic.The computing of related functions of copulas such as cumulative distribution functions,Hfunctions and inverse H-functions often meets with the problem of overflow.We solve this problem by reinvestigating the following six families of bivariate copulas:Normal,Student t,Clayton,Gumbel,Frank and Joe’s copulas.Approximations of the above related functions of copulas are given when the overflow occurs in the computation.All these are implemented in a subpackage bvcopula,in which subroutines are written in Fortran and wrapped into Python and,hence,good performance is guaranteed.
基金supported by National Key R&D Program of China(No.2018YFB0904200)eponymous Complement S&T Program of State Grid Corporation of China(No.SGLNDKOOKJJS1800266).
文摘Owing to the uncertainty and volatility of wind energy,forecasted wind power scenarios with proper spatio-temporal correlations are needed in various decision-making problems involving power systems.In this study,forecasted scenarios are generated from an estimated multi-variate distribution of multiple regional wind farms.According to the theory of copulas,marginal distributions and the dependence structure of multi-variate distribution are modeled through the proposed distance-weighted kernel density estimation method and the regular vine(R-vine)copula,respectively.Owing to the flexibility of decomposing correlations of high dimensions into different types of pair-copulas,the R-vine copula provides more accurate results in describing the complicated dependence of wind power.In the case of 26 wind farms located in East China,highquality forecasted scenarios as well as the corresponding probabilistic forecasting and point forecasting results are obtained using the proposed method,and the results are evaluated using a comprehensive verification framework.
文摘碳排放交易市场的建立,是一个基于经济学理论来解决气候变暖问题的具有价值的途径,其目的是发展低碳经济。在欧盟排放交易体系一级市场上,以欧盟排放配额(European Union Allowances,EUA)作为主要交易标的物的碳排放权交易市场已经成为一个重要的新兴贸易市场。随着碳排放权交易市场的不断发展,该市场的资本化程度逐渐深化,其金融属性也日益显著,并逐步融入到国际资本市场体系之中。与其它资本市场相类似,碳排放权交易市场之间也存在着复杂的非线性相关关系,而Copula函数可以用来捕捉这种相依结构特征。因此,文章选取欧盟排放配额(EUA)期货的日价格时间序列数据,首先假设新息序列服从学生t分布,运用ARMA-GARCH模型对经调整的对数收益率序列进行过滤,采用极大似然方法估计模型的参数,并得到残差序列,同时将其标准化而得到标准化残差;然后,将Kendall’s tau秩相关系数作为权重,采用最大生成树算法(maximum spanning tree algorithm)的序贯Copula选择方法构建合适的规则藤Copula模型,并运用基于序贯的极大似然方法估计规则藤Copula模型,以描述碳排放权交易市场之间复杂的相依结构特征。研究结果发现:在无条件下,t-copula函数可以较好地捕捉碳排放权市场之间的相依关系,说明市场存在明显的对称尾部;在Dec10EUA、Dec12EUA、Dec13EUA市场相依结构固定下,Dec11EUA与Dec14EUA市场之间的相依结构可以采用Gaussian copula函数来描述,而在Dec10EUA、Dec13EUA市场相依结构确定不变情形下,Dec12EUA与Dec14EUA市场之间的相依结构则适合采用Frank copula函数来捕捉,说明这些市场之间并没有出现尾部特征。进一步地,文章分别选择White信息矩阵等式拟合优度检验和基于概率积分转换(probability integral transform,PIT)与经验Copula过程(empirical copula process,ECP)混合方法的拟合优度检验,并基于Bootstrap方法,以Cramer von Mises(Cv M)检验统计量作为度量测度,来对模型进行拟合优度的检验。研究发现,构建的规则藤Copula模型能够较好地捕捉碳排放权市场之间的相依结构。这一研究结果,为准确探讨碳排放权交易市场之间、碳排放权交易市场与其它资本市场之间套期保值策略提供了一定的参考意义,也有利于提高碳排放权市场产品定价的准确度。
基金This work was supported by the National Key Research and Development Program of China(No.2017YFB0902600).
文摘Scenario forecasting methods have been widely studied in recent years to cope with the wind power uncertainty problem. The main difficulty of this problem is to accurately and comprehensively reflect the time-series characteristics and spatial-temporal correlation of wind power generation. In this paper, the marginal distribution model and the dependence structure are combined to describe these complex characteristics. On this basis, a scenario generation method for multiple wind farms is proposed. For the marginal distribution model, the autoregressive integrated moving average-generalized autoregressive conditional heteroskedasticity-t (ARIMA-GARCH-t) model is proposed to capture the time-series characteristics of wind power generation. For the dependence structure, a time-varying regular vine mixed Copula (TRVMC) model is established to capture the spatial-temporal correlation of multiple wind farms. Based on the data from 8 wind farms in Northwest China, sufficient scenarios are generated. The effectiveness of the scenarios is evaluated in 3 aspects. The results show that the generated scenarios have similar fluctuation characteristics, autocorrelation, and crosscorrelation with the actual wind power sequences.
