In order to describe the volatility relationship in the different stages between financial variables，this paper introduces markov conversion mechanism into vector GARCH model to construct the vector MRS-GARCH model． The paper derives aparameter estimation method of this model with filtering technology，then studies the persistence of the vector process based on the prediction equation． Next this article explores the persistence of vector MRS-GARCH model from two aspects of the state duration time and the persistent of vector GARCH process with markov chain，then puts forward exponential decay rate of the vector MRS-GARCH． Afterward，the theorem that satisfied coordination of persistent of vector MRS-GARCH process is given and proved，which can analyze the specific association of financial variables at different stages，and derive the re-gime-swithing linkages between various financial variables． In the end，this essay uses the vector MRS-GARCH model to empirically research on Shanghai and Shenzhen stock yield rates，then confirmes that the two stock markets exizsted co-peresitence after considering state transition．