本文对几种多维GARCH模型的波动持续性及协同持续性条件进行了分析和研究,得出正交GARCH、广义正交GARCH、完全因子GARCH过程的协同持续与各分量波动过程的协整存在密切的关系,而Hadamard乘积GARCH过程不存在协同持续,BEKKGARCH过程在因子模型的表达下存在协同持续,常奈件相关GARCH过程不存在因子表达等结论.
It is studied in this paper that what is the conditions of persistence and co-persistenee in volatilily of multivariate GARCH models. It is showed that there is close relationship between co- persistence in volatility and cointegration of every component volatility processes for orthogonal GARCH, general orthogonal GARCH and full factor GARCH models. Meanwhile, it is proved that there is not co-persistence in volatility for Hadamand GARCH model, but the co-persistence in volatility exists for BEKK GARCH model under factor expression . In addition, it is also discussed that constant conditional correlation GARCH model can not be expressed as factor model.