RESEARCH ON RELATIONSHIP OF VOLATILITY MODELS

摘要

The paper investigated the relationship between ARCH and SV models which are widely used in the analyzing of economical and financial time series. By using stochastical differential equation, we compared GARCH model with SV model and indicated that a discrete time EGARCH(1, 1) process one to one reflects a discrete time SV process under the condition of weakly GRACH process. Moreover, we also discussed the problem of unit roots which exist in EGARCH (1, 1) model and SV model and presented the new conclusions in which the unit roots of two models are reflected each other. In other words, the persistence between the models can be conveyed by stochastically differential equation. The property indicates that there are inherent relationship between the two models.