上次对角双线性时间序列模型的近似三阶矩结构和双谱密度  

The Approximate Third-order Moments and Bispectral Density of USDBL Model

作　　者：王海斌[1] 韦博成[1] 陈浩球[1] 

机构地区：[1]东南大学数学系

出　　处：《数学进展》2004年第2期203-214,共12页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10371016);国家社会科学基金(No.02BTJ001)

摘　　要：本文讨论一类特殊的双线性时间序列模型,该模型中,每一个双线性项均为两个相关的随机变量的乘积,该模型的二阶结构(自协方差和谱)目前已经很清楚了,同线性ARMA模型类似,亦具有有理谱密度,理论上,为了识别该模型,通常是考虑三阶结构(三阶矩和双谱),但由于该模型的复杂性,精确的三阶结构是无法求出的,本文给出一种计算近似三阶矩的公式,由此得到了近似的双谱密度,仿真计算验证了这种方法是有效的。This paper is devoted to investigate a kind of bilinear time series model, in wnich each bilinear term is the production of two correlative random variables. The second order structure of the model(i.e, auto-covariance and spectrum) had been studied by several authors and showed that it was similar to an ARMA model. Because of this, the third order structure(i.e, third order moments and bi-spectum) should be discussed in order to identify the model better. In this paper, the approximate third order structure is evaluated for the model. Simulation verifies that the method is feasible.

关 键 词：上次对角双线性时间序列模型 近似三阶矩结构 双谱密度 自协方差 差分方程 

分 类 号：O211.61[理学—概率论与数理统计]