Properties And Application Of Square Root Stochastic Autoregressive Volatility Model

To get better description of financial time series that have High Kurtosis and Fat Tail and volatility of aggregate, people that study time series models continue to improve, develop and produce a GARCH(generalized autoregressive conditional heteroskedasticity) model, but GARCH model is not closed at temporal aggregation.thus the weak GARCH models developed from GARCH is closed at temporal aggregation. However, it did not consider the risk that measure with conditional variance. And weak GARCH model can not describe the leverage and skewness. To cover the shortage of weak GARCH models, Meddahi and Renault(2000) [1] proposed square-root stochastic autoregressive volatility model based on semi-parametric method. the model has many advantages that weak GARCH models do not. The model is better at inclusivity, and include a lot of available models currently.Firstly, the square-root stochastic autoregressive volatility model was introduced. Then the multiperiod conditional moment restrictions, leverage and skewness and polymeric nature was proved. Meanwhile the paper discussed the relationship between SRSARV model with ARCH(autoregressive conditional heteroskedasticity) model,(semi-strong / weak / asymmetric) GARCH model and the SV(stochastic volatility) model. We use maximum likelihood function based on kalman filters and state-space expression constructs to estimate parameters of SRSARV. At last we use Shanghai index as a sample, model parameters was estimated. the fitting and forecasting results indicate model is good.