ARCH模型与SV模型之间的关系研究

讨论了在金融时间序列中广泛应用的两类波动性模型，即自回归条件异方差(ARCH)模型和随机波动(SV)模型的关系问题。通过随机微分方程研究了GARCH模型和SV模型的相互联系并得到结论：一个离散的EGARCH(1，1)模型在弱GARCH过程的条件下与一个离散的SV模型是一一对应的。在此基础上进一步讨论了EGARCH(1，1)模型和SV模型的单位根问题，结果表明，两类模型的单位根存在对应的关系，即二者的持续性能够通过随机报分方程的形式来传递，这一性质表明了二者之间存在本质的联系。

Research on relationship between ARCH and SV models

In this paper, the relationship between ARCH models and SV models which are widely applied in analyzing of financial time series is studied. By using stochastic differential equation we show that a discrete time EGARCH (1,1) model one by one corresponds to a discrete time SV model. Moreover, we discuss the problem of unit root of these models and conclude that there exists no correspondent relationship between the two types of models, i.e. the persistence existing in the two types of the models can be converted each other. The property indicates that there is essential relationship between the two types of models.