Research On The Volatility Of Stock Fund And Securities Fund Return By ARMA-ARCH Models

In modern finance market, we found that most of the time-series, such as stock price, ratio, securities price, fund price return and so on, the error series were non-autocorrelation, but the squared error series were autocorrelation, which indicate the variance or volatility were time-varying. But the OLS supposes the error series are non-autocorrelation and variances are consistent. So now OLS is not fit for making models and estimation for such economic variables. Auto Regressive Conditional Heteroscedasticity model catches the characters of this kind of economic variables. ARCH model is a kind of dynamic non-linear time series model. It reflects a special feature of economic variables-time-varying variances. Now ARCH model is being widely used in analysis of financial time series fields.The advantages and drawbacks of the family of GARCH models in simulating the volatility of financial markets were investigated by exploring the statistical structure of GARCH models. The GARCH models are proposed, where the stable Paretian distribution is replaced by normal Gaussian distribution. Finally, using the samples of the close prices of the stock fund and securities fund index from CITIC Fund Management Co., Ltd., we discussed the distribution of the rate of return in our fund market with the ARMA(m, n)-EGARCH(p, q) model and ARMA(m, n)-TGARCH(p, q) model. This paper provides a new approach to establish time series model for financial volatility with time-varying variance, describing the sequence characteristics of the Fund. We use Jarque-Bera test method for the data normality test; DF method for unit root test; Lagrange multiplier method for conditional heteroscedasticity test; AIC rule for the model order and Maximum Likelihood estimators for the parameter estimate.The result show that there are significantly volatility, excess kurtosis and heteroscedasticity, persistence and asymmetric effect in our Securities Investment Fund Market. The parameter estimation method and structure of the ARMA-ARCH models were discussed in depth in this paper. The proposed model in this paper has a superior performance in empirical analysis compared with the previous model.