中文摘要：

为了更好地描述存在结构转换的时间序列的波动性，将马尔科夫链和状态转换机制引入GARCH模型，定义了MRS-GARCH模型，使GARCH模型的预测精度和持续性问题得到改善。鉴于还没有MRS-GARCH模型的稳定性和矩的存在性的相关研究，因此，基于马尔科夫链的理论以及几何遍历性和有限矩的简单假设，并使用漂移函数阐述了MRS-GARCH的稳定性和矩的存在性的充分条件。

英文摘要：

In order to better describe the present volatility time series structure transformation,the Markoff chain and state transition mechanism is introduced into the GARCH model,the MRS-GARCH model is defined,the prediction accuracy and continuity of the improved GARCH model. In view of the fact that there is no related research, the stability of MRS-GARCH model and the moment so, Markov chain theory and the simple hypothesis geometric ergodicity and finite moments based, and use the drift function describes the sufficient conditions for the existence and stability of MRS-GARCH and moments.