混合自回归模型自协方差函数绝对可和的探讨

摘要

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．%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.