ARMA模型平稳解存在性问题的一些研究  

Some Results on the Existence of Stationary Solutions to ARMA Models

作　　者：马新生[1] 胡文玉[1] 翁瑾[1] 刘县明[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2009年第3期214-218,223,共6页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(2007GZS2398);南昌大学研究生创新专项资金资助

摘　　要：ARMA模型是现代时间序列分析中最为常用的模型之一,在科学研究和工程系统中具有广泛的运用。AR-MA模型使用的前提条件是,建立的时间序列是由一个零均值的平稳随机过程所产生的,即其存在性能够得到保证。基于此,详细讨论了所有情形下AR模型及ARMA模型平稳解的存在性条件,然后将一维ARMA模型的渐进平稳性转化为向量AR模型的平稳性,从而给出了ARMA模型存在渐进平稳解的充分条件。ARMA model is one of the most common models in the modern time series analysis which is widely used in scientific researches and engineering systems. However, the precondition of applying ARMA model is that the established time -series model must be generated from a zero -mean and stationary stochastic process, say, the existence of the solution to the ARMA model. Based on this, the existence of the stationary solutions to ARMA model and AR model is studied in detail firstly, and then the sufficient conditions for the existence of asymptotic stationary solutions to the ARMA model are given,which is obtained by transforming the case of one dimensional ARMA model to the case of vector AR model.

关 键 词：时序模型 ARMA模型 AR模型 平稳解 渐进平稳解 

分 类 号：O21[理学—概率论与数理统计]