多变量Copula函数在干旱风险分析中的应用进展

Application progress of multi-variable Copula function in drought risk analysis

Copula是一种构造多元联合分布和分析随机变量间相关结构的重要工具。对2005年以来国内外学者对Copula在干旱领域的研究和应用进行了综述,阐述了当前Copula方法存在的问题和继续研究方向。首先,高维Copula函数的参数估计不够精确,虽然高维Copula构造方法如嵌套法、混合法、条件混合法等对参数估计有本质上的简化作用、基于Bayesian理论的Copula参数估计方法比传统方法有明显改进,但在计算量、置信水平、样本量等需求上仍存在取舍,高维Copula理论的参数估计方法仍是Copula理论研究中的难点;其次,干旱特征对时间具有较强敏感性,使得Copula函数应用于干旱问题需要具有时变性,时变和空间变化Copula理论能综合时空维度对干旱进行全面分析,这将是未来Copula研究的方向之一;最后,Copula方法能被应用于诸多方向,还需要更加发散地将Copula方法与其他框架相结合。

Copula is an important tool for structuring the multivariate joint distribution and analyzing the correlation structure between random variables.This paper reviews the research and application of Copula in drought since 2005 and discusses the current problems of Copula method and the development direction of Copula theory.Firstly,the parameter estimation of high-dimensional Copula function is not accurate enough.Although the high-dimensional Copula construction methods such as nested method,hybrid method,and condition-hybrid method can essentially simplify parameter estimation,and the Copula parameter estimation method based on Bayesian theory is a significant improvement over the traditional method,still they cannot deliver satisfactory computation amount,confidence level,and sample size at the same time.The parameter estimation method of highdimensional Copula theory is still a difficult point in the research of Copula theory.Secondly,the characteristics of drought are sensitive to time;thus,the Copula function needs to be time-varying in order to be applied to drought problems.The Copula theory with temporal and spatial variation can be used to analyze drought.It is one of the future directions of Copula research.Thirdly,Copula method can be applied in a number of directions,and also need to be further combined with other frameworks.