南京工程学院学报：自然科学版
南京工程學院學報：自然科學版
남경공정학원학보：자연과학판
Journal of Nanjing Institute of Technology :Natural Science Edition
2012年
4期
1-4
,共4页
混合自回归模型%自协方差函数%特征方程%绝对可和
混閤自迴歸模型%自協方差函數%特徵方程%絕對可和
혼합자회귀모형%자협방차함수%특정방정%절대가화
mixture autoregressive model%auto-covariance function%characteristic equation%absolutely summable
AR（自回归）模型平稳的充分必要条件是自协方差函数绝对可和，而自协方差函数绝对可和的充要条件又是自协方差函数满足的特征方程所对应的特征根全位于单位圆外．本文证明了在某种特定情形下MAR（混合自回归）模型自协方差函数绝对可和的充要条件是其自协方差函数满足的特征方程所对应的特征根全位于单位圆外，为平稳性的进一步研究获得了一些重要的结果．
AR（自迴歸）模型平穩的充分必要條件是自協方差函數絕對可和，而自協方差函數絕對可和的充要條件又是自協方差函數滿足的特徵方程所對應的特徵根全位于單位圓外．本文證明瞭在某種特定情形下MAR（混閤自迴歸）模型自協方差函數絕對可和的充要條件是其自協方差函數滿足的特徵方程所對應的特徵根全位于單位圓外，為平穩性的進一步研究穫得瞭一些重要的結果．
AR（자회귀）모형평은적충분필요조건시자협방차함수절대가화，이자협방차함수절대가화적충요조건우시자협방차함수만족적특정방정소대응적특정근전위우단위원외．본문증명료재모충특정정형하MAR（혼합자회귀）모형자협방차함수절대가화적충요조건시기자협방차함수만족적특정방정소대응적특정근전위우단위원외，위평은성적진일보연구획득료일사중요적결과．
The sufficient and necessary condition for stationarity regarding autoregressive model is absolutely summable of auto-covariance function, while that condition for auto-covariance function's absolutely summable is that all characteristic roots of characteristic equation corresponding to auto-covariance function are spread out of unit circle. This paper proves that, under some special circumstance, the sufficient and necessary condition for absolutely summable about mixture autoregressive model's auto-covariance function is that all characteristic roots of characteristic equation corresponding to auto-covariance function are spread out of unit circle. The result is conducive to further research into the stationarity of this model.
