基于分位数与耦合诊断平稳随机过程相依性

Dependence diagnosis for stationary stochastic processes based on both quantiles and copulas

基于分位数和耦合的概念,本文提出平稳随机过程分位数-耦合交叉协方差函数的概念.该函数可以描述平稳过程的时间可逆性、状态相依性以及在二阶矩不存在时的长程相依性等自协方差函数无法刻画的过程特征.本文讨论了平稳随机过程分位数-耦合交叉协方差函数的一些基本性质;基于离散抽样,给出了分位数-耦合交叉协方差函数的估计量,并证明了其相合性;利用文中估计方法,对具有相同一维平稳边际分布和自协方差函数的不同类型随机过程(Gamma-OU (Ornstein-Uhlenbeck)过程和CIR (Cox-Ingersoll-Ross)模型)的分位数-耦合交叉协方差函数进行比较,得到了其自相依性质的差别.最后,将估计方法应用于船体振动序列自相依性质分析,为船体振动模型选择提供借鉴.

Based on both quantiles and copulas,a new concept,the quantile-copula cross-covariance function,for stationary stochastic processes,is given.The function can capture many dependence characteristics that the traditional auto-covariance function cannot cover,such as time reversibility,state dependence as well as long-range dependence when the auto-covariance function does not exist.A consistent estimator of the quantile-copula crosscovariance function is proposed based on discretely sampled stationary processes.By comparing the estimated quantile-copula cross-covariance functions,the dependence differences are distinguished for two types of processes,Gamma-OU processes and CIR models,which have the common one-dimensional stationary marginal distribution and the common auto-covariance function.By analyzing the estimated quantile-copula cross-covariance function of a ship vibration series,some suggestions for modeling the vibration process are provided.